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- La ecuación:
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Ecuación x^2-11*x+30=0
- Ecuación x^2+y^2=9
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Ecuación -33-y=-19
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Ecuación 11/(x-9)=-10
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -4*x+6*y=-7
- -7*x-13*y=5
- -18*x+8*y=-2
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Expresiones idénticas
- x^ cuatro - cuatro *(x^ tres)*y+ dos *(x^ dos)*(y^ dos)- cuatro *x*(y^ tres)+y^ cuatro - cero ,8y= cero
- x en el grado 4 menos 4 multiplicar por (x al cubo ) multiplicar por y más 2 multiplicar por (x al cuadrado ) multiplicar por (y al cuadrado ) menos 4 multiplicar por x multiplicar por (y al cubo ) más y en el grado 4 menos 0,8y es igual a 0
- x en el grado cuatro menos cuatro multiplicar por (x en el grado tres) multiplicar por y más dos multiplicar por (x en el grado dos) multiplicar por (y en el grado dos) menos cuatro multiplicar por x multiplicar por (y en el grado tres) más y en el grado cuatro menos cero ,8y es igual a cero
- x4-4*(x3)*y+2*(x2)*(y2)-4*x*(y3)+y4-0,8y=0
- x4-4*x3*y+2*x2*y2-4*x*y3+y4-0,8y=0
- x⁴-4*(x³)*y+2*(x²)*(y²)-4*x*(y³)+y⁴-0,8y=0
- x en el grado 4-4*(x en el grado 3)*y+2*(x en el grado 2)*(y en el grado 2)-4*x*(y en el grado 3)+y en el grado 4-0,8y=0
- x^4-4(x^3)y+2(x^2)(y^2)-4x(y^3)+y^4-0,8y=0
- x4-4(x3)y+2(x2)(y2)-4x(y3)+y4-0,8y=0
- x4-4x3y+2x2y2-4xy3+y4-0,8y=0
- x^4-4x^3y+2x^2y^2-4xy^3+y^4-0,8y=0
- x^4-4*(x^3)*y+2*(x^2)*(y^2)-4*x*(y^3)+y^4-0,8y=O
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Expresiones semejantes
- x^4-4*(x^3)*y+2*(x^2)*(y^2)-4*x*(y^3)+y^4+0,8y=0
- x^4-4*(x^3)*y+2*(x^2)*(y^2)-4*x*(y^3)-y^4-0,8y=0
- x^4-4*(x^3)*y+2*(x^2)*(y^2)+4*x*(y^3)+y^4-0,8y=0
- x^4+4*(x^3)*y+2*(x^2)*(y^2)-4*x*(y^3)+y^4-0,8y=0
- x^4-4*(x^3)*y-2*(x^2)*(y^2)-4*x*(y^3)+y^4-0,8y=0
x^4-4*(x^3)*y+2*(x^2)*(y^2)-4*x*(y^3)+y^4-0,8y=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 3 2 2 3 4 4*y
x - 4*x *y + 2*x *y - 4*x*y + y - --- = 0
5
$$- \frac{4 y}{5} + \left(y^{4} + \left(- 4 x y^{3} + \left(2 x^{2} y^{2} + \left(x^{4} - 4 x^{3} y\right)\right)\right)\right) = 0$$
Gráfica
Respuesta rápida
[src]
// _______________________________________________________________________________________________________________ \ // _______________________________________________________________________________________________________________ \
|| / ________________________________ | || / ________________________________ |
|| / / 2 / 4 4*y\ | || / / 2 / 4 4*y\ |
|| / / 6 4*y *|- 4*y - ---| 2 3 | || / / 6 4*y *|- 4*y - ---| 2 3 |
|| / / 200*y \ 5 / 16*y 16*y | || / / 200*y \ 5 / 16*y 16*y |
|| / 2*3 / - ------ - ------------------- + ----- - ---------------------------------------------------------- | || / 2*3 / - ------ - ------------------- + ----- - ---------------------------------------------------------- |
|| ___________________________________________________ / \/ 27 3 3 ___________________________________________________ | || ___________________________________________________ / \/ 27 3 3 ___________________________________________________ |
|| / ________________________________ / / ________________________________ | || / ________________________________ / / ________________________________ |
|| / / 2 / 4 4*y\ / / / 2 / 4 4*y\ | || / / 2 / 4 4*y\ / / / 2 / 4 4*y\ |
|| / / 6 4*y *|- 4*y - ---| 2 / / / 6 4*y *|- 4*y - ---| 2 | || / / 6 4*y *|- 4*y - ---| 2 / / / 6 4*y *|- 4*y - ---| 2 |
|| / / 200*y \ 5 / 8*y / / / 200*y \ 5 / 8*y | || / / 200*y \ 5 / 8*y / / / 200*y \ 5 / 8*y |
|| / - 2*3 / - ------ - ------------------- + ---- / / - 2*3 / - ------ - ------------------- + ---- 4 | || / - 2*3 / - ------ - ------------------- + ---- / / - 2*3 / - ------ - ------------------- + ---- 4 |
|| \/ \/ 27 3 3 \/ \/ \/ 27 3 3 4*y 8*y | || \/ \/ 27 3 3 \/ \/ \/ 27 3 3 4*y 8*y |
|| y - ---------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- for --- + ---- = 0| || y - ---------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- for --- + ---- = 0|
|| 2 2 5 3 | || 2 2 5 3 |
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|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
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|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 3 2*|--- + ----| | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 3 2*|--- + ----| |
x1 = I*im|< / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 16*y 16*y \ 5 3 / | + re|< / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 16*y 16*y \ 5 3 / |
|| / - 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ----- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- | || / - 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ----- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 27 3 3 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 27 3 3 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________ / / _____________________________________________________________________________________________ / ___________________________________________________ | || / _____________________________________________________________________________________________ / / _____________________________________________________________________________________________ / ___________________________________________________ |
|| / / ___________________________________________________ / / / ___________________________________________________ / / 2 | || / / ___________________________________________________ / / / ___________________________________________________ / / 2 |
|| / / / 2 / / / / 2 / / / 2 / 4 4*y\\ 3 | || / / / 2 / / / / 2 / / / 2 / 4 4*y\\ 3 |
|| / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 / / | 6 4*y *|- 4*y - ---|| / 4\ | || / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 / / | 6 4*y *|- 4*y - ---|| / 4\ |
|| / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ | || / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |
|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / \ 27 3 / \ 5 3 / 100*y \ 5 / | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / \ 27 3 / \ 5 3 / 100*y \ 5 / |
|| / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- | || / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- |
|| / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- / / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- \/ \/ 4 27 27 3 | || / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- / / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- \/ \/ 4 27 27 3 |
|| / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ / / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ | || / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ / / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ |
|| / / ___________________________________________________ / / / ___________________________________________________ | || / / ___________________________________________________ / / / ___________________________________________________ |
|| / / / 2 / / / / 2 | || / / / 2 / / / / 2 |
|| / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 | || / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 |
|| / / / | 6 4*y *|- 4*y - ---|| / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ | || / / / | 6 4*y *|- 4*y - ---|| / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ |
|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| |
|| / / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / | || / / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / |
|| / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- | || / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- |
|| \/ \/ \/ 4 27 27 3 \/ \/ \/ \/ 4 27 27 3 | || \/ \/ \/ 4 27 27 3 \/ \/ \/ \/ 4 27 27 3 |
||y - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||y - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
|| 2 2 | || 2 2 |
\\ / \\ /
$$x_{1} = \operatorname{re}{\left(\begin{cases} y - \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} - \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y - \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} y - \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} - \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y - \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// _______________________________________________________________________________________________________________ \ // _______________________________________________________________________________________________________________ \
|| / ________________________________ | || / ________________________________ |
|| / / 2 / 4 4*y\ | || / / 2 / 4 4*y\ |
|| / / 6 4*y *|- 4*y - ---| 2 3 | || / / 6 4*y *|- 4*y - ---| 2 3 |
|| / / 200*y \ 5 / 16*y 16*y | || / / 200*y \ 5 / 16*y 16*y |
|| / 2*3 / - ------ - ------------------- + ----- - ---------------------------------------------------------- | || / 2*3 / - ------ - ------------------- + ----- - ---------------------------------------------------------- |
|| / \/ 27 3 3 ___________________________________________________ ___________________________________________________ | || / \/ 27 3 3 ___________________________________________________ ___________________________________________________ |
|| / / ________________________________ / ________________________________ | || / / ________________________________ / ________________________________ |
|| / / / 2 / 4 4*y\ / / 2 / 4 4*y\ | || / / / 2 / 4 4*y\ / / 2 / 4 4*y\ |
|| / / / 6 4*y *|- 4*y - ---| 2 / / 6 4*y *|- 4*y - ---| 2 | || / / / 6 4*y *|- 4*y - ---| 2 / / 6 4*y *|- 4*y - ---| 2 |
|| / / / 200*y \ 5 / 8*y / / 200*y \ 5 / 8*y | || / / / 200*y \ 5 / 8*y / / 200*y \ 5 / 8*y |
|| / / - 2*3 / - ------ - ------------------- + ---- / - 2*3 / - ------ - ------------------- + ---- 4 | || / / - 2*3 / - ------ - ------------------- + ---- / - 2*3 / - ------ - ------------------- + ---- 4 |
|| \/ \/ \/ 27 3 3 \/ \/ 27 3 3 4*y 8*y | || \/ \/ \/ 27 3 3 \/ \/ 27 3 3 4*y 8*y |
|| y + ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------- for --- + ---- = 0| || y + ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------- for --- + ---- = 0|
|| 2 2 5 3 | || 2 2 5 3 |
|| | || |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________ | || / _____________________________________________________________________________________________ |
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|| / / / 2 | || / / / 2 |
|| / / / / 2 / 4 4*y\\ 3 | || / / / / 2 / 4 4*y\\ 3 |
|| / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ | || / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ |
|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 3 2*|--- + ----| | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 3 2*|--- + ----| |
x2 = I*im|< / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 16*y 16*y \ 5 3 / | + re|< / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 16*y 16*y \ 5 3 / |
|| / - 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ----- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- | || / - 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ----- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- |
|| / \/ \/ 4 27 27 3 3 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________ ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / \/ \/ 4 27 27 3 3 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________ ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / _____________________________________________________________________________________________ / ___________________________________________________ / _____________________________________________________________________________________________ | || / / _____________________________________________________________________________________________ / ___________________________________________________ / _____________________________________________________________________________________________ |
|| / / / ___________________________________________________ / / 2 / / ___________________________________________________ | || / / / ___________________________________________________ / / 2 / / ___________________________________________________ |
|| / / / / 2 / / / 2 / 4 4*y\\ 3 / / / 2 | || / / / / 2 / / / 2 / 4 4*y\\ 3 / / / 2 |
|| / / / / / 2 / 4 4*y\\ 3 / / | 6 4*y *|- 4*y - ---|| / 4\ / / / / 2 / 4 4*y\\ 3 | || / / / / / 2 / 4 4*y\\ 3 / / | 6 4*y *|- 4*y - ---|| / 4\ / / / / 2 / 4 4*y\\ 3 |
|| / / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ | || / / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ |
|| / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | | || / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | |
|| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| | || / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| |
|| / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / | || / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / |
|| / / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- \/ \/ 4 27 27 3 / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- | || / / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- \/ \/ 4 27 27 3 / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- |
|| / / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ | || / / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ |
|| / / / ___________________________________________________ / / ___________________________________________________ | || / / / ___________________________________________________ / / ___________________________________________________ |
|| / / / / 2 / / / 2 | || / / / / 2 / / / 2 |
|| / / / / / 2 / 4 4*y\\ 3 / / / / 2 / 4 4*y\\ 3 | || / / / / / 2 / 4 4*y\\ 3 / / / / 2 / 4 4*y\\ 3 |
|| / / / / | 6 4*y *|- 4*y - ---|| / 4\ / / / | 6 4*y *|- 4*y - ---|| / 4\ | || / / / / | 6 4*y *|- 4*y - ---|| / 4\ / / / | 6 4*y *|- 4*y - ---|| / 4\ |
|| / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ | || / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |
|| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| | || / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| |
|| / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / | || / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / |
|| / / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- | || / / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- |
|| \/ \/ \/ \/ 4 27 27 3 \/ \/ \/ 4 27 27 3 | || \/ \/ \/ \/ 4 27 27 3 \/ \/ \/ 4 27 27 3 |
||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
|| 2 2 | || 2 2 |
\\ / \\ /
$$x_{2} = \operatorname{re}{\left(\begin{cases} y - \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} + \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y - \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} y - \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} + \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y - \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// _______________________________________________________________________________________________________________ \ // _______________________________________________________________________________________________________________ \
|| / ________________________________ | || / ________________________________ |
|| / / 2 / 4 4*y\ | || / / 2 / 4 4*y\ |
|| / / 6 4*y *|- 4*y - ---| 2 3 | || / / 6 4*y *|- 4*y - ---| 2 3 |
|| / / 200*y \ 5 / 16*y 16*y | || / / 200*y \ 5 / 16*y 16*y |
|| / 2*3 / - ------ - ------------------- + ----- + ---------------------------------------------------------- | || / 2*3 / - ------ - ------------------- + ----- + ---------------------------------------------------------- |
|| ___________________________________________________ / \/ 27 3 3 ___________________________________________________ | || ___________________________________________________ / \/ 27 3 3 ___________________________________________________ |
|| / ________________________________ / / ________________________________ | || / ________________________________ / / ________________________________ |
|| / / 2 / 4 4*y\ / / / 2 / 4 4*y\ | || / / 2 / 4 4*y\ / / / 2 / 4 4*y\ |
|| / / 6 4*y *|- 4*y - ---| 2 / / / 6 4*y *|- 4*y - ---| 2 | || / / 6 4*y *|- 4*y - ---| 2 / / / 6 4*y *|- 4*y - ---| 2 |
|| / / 200*y \ 5 / 8*y / / / 200*y \ 5 / 8*y | || / / 200*y \ 5 / 8*y / / / 200*y \ 5 / 8*y |
|| / - 2*3 / - ------ - ------------------- + ---- / / - 2*3 / - ------ - ------------------- + ---- 4 | || / - 2*3 / - ------ - ------------------- + ---- / / - 2*3 / - ------ - ------------------- + ---- 4 |
|| \/ \/ 27 3 3 \/ \/ \/ 27 3 3 4*y 8*y | || \/ \/ 27 3 3 \/ \/ \/ 27 3 3 4*y 8*y |
|| y + ---------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- for --- + ---- = 0| || y + ---------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- for --- + ---- = 0|
|| 2 2 5 3 | || 2 2 5 3 |
|| | || |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________ | || / _____________________________________________________________________________________________ |
|| / / ___________________________________________________ | || / / ___________________________________________________ |
|| / / / 2 | || / / / 2 |
|| / / / / 2 / 4 4*y\\ 3 | || / / / / 2 / 4 4*y\\ 3 |
|| / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ | || / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ |
|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 3 2*|--- + ----| | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 3 2*|--- + ----| |
x3 = I*im|< / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 16*y 16*y \ 5 3 / | + re|< / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 16*y 16*y \ 5 3 / |
|| / - 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ----- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- | || / - 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ----- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 27 3 3 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 27 3 3 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________ / / _____________________________________________________________________________________________ / ___________________________________________________ | || / _____________________________________________________________________________________________ / / _____________________________________________________________________________________________ / ___________________________________________________ |
|| / / ___________________________________________________ / / / ___________________________________________________ / / 2 | || / / ___________________________________________________ / / / ___________________________________________________ / / 2 |
|| / / / 2 / / / / 2 / / / 2 / 4 4*y\\ 3 | || / / / 2 / / / / 2 / / / 2 / 4 4*y\\ 3 |
|| / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 / / | 6 4*y *|- 4*y - ---|| / 4\ | || / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 / / | 6 4*y *|- 4*y - ---|| / 4\ |
|| / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ | || / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |
|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / \ 27 3 / \ 5 3 / 100*y \ 5 / | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / \ 27 3 / \ 5 3 / 100*y \ 5 / |
|| / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- | || / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- |
|| / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- / / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- \/ \/ 4 27 27 3 | || / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- / / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- \/ \/ 4 27 27 3 |
|| / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ / / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ | || / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ / / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ |
|| / / ___________________________________________________ / / / ___________________________________________________ | || / / ___________________________________________________ / / / ___________________________________________________ |
|| / / / 2 / / / / 2 | || / / / 2 / / / / 2 |
|| / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 | || / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 |
|| / / / | 6 4*y *|- 4*y - ---|| / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ | || / / / | 6 4*y *|- 4*y - ---|| / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ |
|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| |
|| / / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / | || / / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / |
|| / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- | || / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- |
|| \/ \/ \/ 4 27 27 3 \/ \/ \/ \/ 4 27 27 3 | || \/ \/ \/ 4 27 27 3 \/ \/ \/ \/ 4 27 27 3 |
||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
|| 2 2 | || 2 2 |
\\ / \\ /
$$x_{3} = \operatorname{re}{\left(\begin{cases} y + \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} - \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y + \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} y + \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} - \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y + \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// _______________________________________________________________________________________________________________ \ // _______________________________________________________________________________________________________________ \
|| / ________________________________ | || / ________________________________ |
|| / / 2 / 4 4*y\ | || / / 2 / 4 4*y\ |
|| / / 6 4*y *|- 4*y - ---| 2 3 | || / / 6 4*y *|- 4*y - ---| 2 3 |
|| / / 200*y \ 5 / 16*y 16*y | || / / 200*y \ 5 / 16*y 16*y |
|| / 2*3 / - ------ - ------------------- + ----- + ---------------------------------------------------------- | || / 2*3 / - ------ - ------------------- + ----- + ---------------------------------------------------------- |
|| ___________________________________________________ / \/ 27 3 3 ___________________________________________________ | || ___________________________________________________ / \/ 27 3 3 ___________________________________________________ |
|| / ________________________________ / / ________________________________ | || / ________________________________ / / ________________________________ |
|| / / 2 / 4 4*y\ / / / 2 / 4 4*y\ | || / / 2 / 4 4*y\ / / / 2 / 4 4*y\ |
|| / / 6 4*y *|- 4*y - ---| 2 / / / 6 4*y *|- 4*y - ---| 2 | || / / 6 4*y *|- 4*y - ---| 2 / / / 6 4*y *|- 4*y - ---| 2 |
|| / / 200*y \ 5 / 8*y / / / 200*y \ 5 / 8*y | || / / 200*y \ 5 / 8*y / / / 200*y \ 5 / 8*y |
|| / - 2*3 / - ------ - ------------------- + ---- / / - 2*3 / - ------ - ------------------- + ---- 4 | || / - 2*3 / - ------ - ------------------- + ---- / / - 2*3 / - ------ - ------------------- + ---- 4 |
|| \/ \/ 27 3 3 \/ \/ \/ 27 3 3 4*y 8*y | || \/ \/ 27 3 3 \/ \/ \/ 27 3 3 4*y 8*y |
|| y + ---------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- for --- + ---- = 0| || y + ---------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- for --- + ---- = 0|
|| 2 2 5 3 | || 2 2 5 3 |
|| | || |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________ | || / _____________________________________________________________________________________________ |
|| / / ___________________________________________________ | || / / ___________________________________________________ |
|| / / / 2 | || / / / 2 |
|| / / / / 2 / 4 4*y\\ 3 | || / / / / 2 / 4 4*y\\ 3 |
|| / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ | || / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ |
|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 3 2*|--- + ----| | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 3 2*|--- + ----| |
x4 = I*im|< / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 16*y 16*y \ 5 3 / | + re|< / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 16*y 16*y \ 5 3 / |
|| / - 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ----- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- | || / - 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ----- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 27 3 3 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 27 3 3 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________ / / _____________________________________________________________________________________________ / ___________________________________________________ | || / _____________________________________________________________________________________________ / / _____________________________________________________________________________________________ / ___________________________________________________ |
|| / / ___________________________________________________ / / / ___________________________________________________ / / 2 | || / / ___________________________________________________ / / / ___________________________________________________ / / 2 |
|| / / / 2 / / / / 2 / / / 2 / 4 4*y\\ 3 | || / / / 2 / / / / 2 / / / 2 / 4 4*y\\ 3 |
|| / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 / / | 6 4*y *|- 4*y - ---|| / 4\ | || / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 / / | 6 4*y *|- 4*y - ---|| / 4\ |
|| / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ | || / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ / 4\ / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |
|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |4*y 8*y | / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / \ 27 3 / \ 5 3 / 100*y \ 5 / | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| 2 2*|--- + ----| / / \ 27 3 / \ 5 3 / 100*y \ 5 / |
|| / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- | || / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / 8*y \ 5 3 / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- |
|| / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- / / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- \/ \/ 4 27 27 3 | || / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- / / 2*3 / / --------------------------------- + ------------- + ------ + ------------------- + ---- - --------------------------------------------------------------------------------------------------------- \/ \/ 4 27 27 3 |
|| / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ / / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ | || / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ / / \/ \/ 4 27 27 3 3 _____________________________________________________________________________________________ |
|| / / ___________________________________________________ / / / ___________________________________________________ | || / / ___________________________________________________ / / / ___________________________________________________ |
|| / / / 2 / / / / 2 | || / / / 2 / / / / 2 |
|| / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 | || / / / / 2 / 4 4*y\\ 3 / / / / / 2 / 4 4*y\\ 3 |
|| / / / | 6 4*y *|- 4*y - ---|| / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ | || / / / | 6 4*y *|- 4*y - ---|| / 4\ / / / / | 6 4*y *|- 4*y - ---|| / 4\ |
|| / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ | || / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ / / / / | 200*y \ 5 /| |4*y 8*y | 2 / 4 4*y\ |
|| / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| | || / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| / / / / |- ------ - -------------------| |--- + ----| 6 2*y *|- 4*y - ---| |
|| / / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / | || / / / \ 27 3 / \ 5 3 / 100*y \ 5 / / / / / \ 27 3 / \ 5 3 / 100*y \ 5 / |
|| / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- | || / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- / / 3*3 / / --------------------------------- + ------------- + ------ + ------------------- |
|| \/ \/ \/ 4 27 27 3 \/ \/ \/ \/ 4 27 27 3 | || \/ \/ \/ 4 27 27 3 \/ \/ \/ \/ 4 27 27 3 |
||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
|| 2 2 | || 2 2 |
\\ / \\ /
$$x_{4} = \operatorname{re}{\left(\begin{cases} y + \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} + \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y + \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} y + \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} + \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y + \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((y + sqrt(8*y^2/3 - 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3))/2 + sqrt(16*y^3/sqrt(8*y^2/3 - 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3)) + 16*y^2/3 + 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3)/2, 8*y^4/3 + 4*y/5 = 0), (y + sqrt(8*y^2/3 - 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3))/2 + sqrt(16*y^3/sqrt(8*y^2/3 - 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 16*y^2/3 + 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) - 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3))/2, True))) + i*im(Piecewise((y + sqrt(8*y^2/3 - 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3))/2 + sqrt(16*y^3/sqrt(8*y^2/3 - 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3)) + 16*y^2/3 + 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3))/2, 8*y^4/3 + 4*y/5 = 0), (y + sqrt(8*y^2/3 - 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3))/2 + sqrt(16*y^3/sqrt(8*y^2/3 - 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 16*y^2/3 + 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) - 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3))/2, True))))