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- La ecuación:
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Ecuación x^4-x^3+5*x^2=0
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Ecuación 3*x+5+(x+5)=(1-x)+4
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Ecuación 3-x/7=x/3
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Ecuación (7-x)^2=(x+16)^2
- Expresar {x} en función de y en la ecuación:
- 10*x+5*y=-17
- -6*x-2*y=-10
- 17*x-11*y=2
- -14*x-3*y=-5
- Integral de d{x}:
- √3
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√3
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Expresiones idénticas
- (5x²+ siete y)²-7(7y²+10xy)x=√ tres
- (5x² más 7y)² menos 7(7y² más 10xy)x es igual a √3
- (5x² más siete y)² menos 7(7y² más 10xy)x es igual a √ tres
- 5x²+7y²-77y²+10xyx=√3
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Expresiones semejantes
- (5x²+7y)²-7(7y²-10xy)x=√3
- (5x²-7y)²-7(7y²+10xy)x=√3
- (5x²+7y)²+7(7y²+10xy)x=√3
(5x²+7y)²-7(7y²+10xy)x=√3 la ecuación
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Solución
Ha introducido
[src]
2 / 2 \ / 2 \ ___ \5*x + 7*y/ - 7*\7*y + 10*x*y/*x = \/ 3
$$- x 7 \left(10 x y + 7 y^{2}\right) + \left(5 x^{2} + 7 y\right)^{2} = \sqrt{3}$$
Gráfica
Respuesta rápida
[src]
// ____________________________________________ \ // ____________________________________________ \
|| / _____ | || / _____ |
|| / 2/3 3 ___ 3 / 4 2/3 3 ___ 2 | || / 2/3 3 ___ 3 / 4 2/3 3 ___ 2 |
|| / 7*5 *\/ 7 *\/ -y 14*5 *\/ 7 *y | || / 7*5 *\/ 7 *\/ -y 14*5 *\/ 7 *y |
|| / --------------------- - ------------------ | || / --------------------- - ------------------ |
|| / 25 ___________ ___________ | || / 25 ___________ ___________ |
|| / / _____ / _____ | || / / _____ / _____ |
|| / / 3 / 4 3 ___ 2/3 / 3 / 4 ___ 2 | || / / 3 / 4 3 ___ 2/3 / 3 / 4 ___ 2 |
|| \/ 25*\/ -\/ -y \/ 5 *7 *\/ -\/ -y \/ 3 49*y | || \/ 25*\/ -\/ -y \/ 5 *7 *\/ -\/ -y \/ 3 49*y |
|| - ----------------------------------------------------- - -------------------------- for - ----- + ----- = 0| || - ----------------------------------------------------- - -------------------------- for - ----- + ----- = 0|
|| 2 10 25 25 | || 2 10 25 25 |
|| | || |
|| ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________ | || / _____________________________________________________ |
|| / / _________________________________ | || / / _________________________________ |
|| / / / 3 | || / / / 3 |
|| / / / / 2 ___\ / 2 ___\ | || / / / / 2 ___\ / 2 ___\ |
|| / / / | 49*y \/ 3 | | 49*y \/ 3 | | || / / / | 49*y \/ 3 | | 49*y \/ 3 | |
|| / / / |- ----- + -----| 8 4 2 2*|- ----- + -----| | || / / / |- ----- + -----| 8 4 2 2*|- ----- + -----| |
|| / / / \ 25 25 / 5764801*y 2401*y 98*y \ 25 25 / | || / / / \ 25 25 / 5764801*y 2401*y 98*y \ 25 25 / |
x1 = I*im|< / - 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------- | + re|< / - 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------- |
|| _____________________________________________________________________________________________________________________________________ / \/ \/ 27 100000000 10000 _____________________________________________________________________________________________________________________________________ _____________________________________________________ | || _____________________________________________________________________________________________________________________________________ / \/ \/ 27 100000000 10000 _____________________________________________________________________________________________________________________________________ _____________________________________________________ |
|| / _____________________________________________________ / / _____________________________________________________ / _________________________________ | || / _____________________________________________________ / / _____________________________________________________ / _________________________________ |
|| / / _________________________________ / / / _________________________________ / / 3 | || / / _________________________________ / / / _________________________________ / / 3 |
|| / / / 3 / / / / 3 / / / 2 ___\ | || / / / 3 / / / / 3 / / / 2 ___\ |
|| / / / / 2 ___\ / 2 ___\ / / / / / 2 ___\ / 2 ___\ / / | 49*y \/ 3 | | || / / / / 2 ___\ / 2 ___\ / / / / / 2 ___\ / 2 ___\ / / | 49*y \/ 3 | |
|| / / / | 49*y \/ 3 | | 49*y \/ 3 | / / / / | 49*y \/ 3 | | 49*y \/ 3 | / / |- ----- + -----| 8 4 | || / / / | 49*y \/ 3 | | 49*y \/ 3 | / / / / | 49*y \/ 3 | | 49*y \/ 3 | / / |- ----- + -----| 8 4 |
|| / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / \ 25 25 / 5764801*y 2401*y | || / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / \ 25 25 / 5764801*y 2401*y |
|| / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / / / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / 3*3 / / ------------------ + ---------- + ------- | || / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / / / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / 3*3 / / ------------------ + ---------- + ------- |
|| / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- / 25* / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- \/ \/ 27 100000000 10000 | || / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- / 25* / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- \/ \/ 27 100000000 10000 |
|| / \/ \/ 27 100000000 10000 _____________________________________________________ / / \/ \/ 27 100000000 10000 _____________________________________________________ | || / \/ \/ 27 100000000 10000 _____________________________________________________ / / \/ \/ 27 100000000 10000 _____________________________________________________ |
|| / / _________________________________ / / / _________________________________ | || / / _________________________________ / / / _________________________________ |
|| / / / 3 / / / / 3 | || / / / 3 / / / / 3 |
|| / / / / 2 ___\ / / / / / 2 ___\ | || / / / / 2 ___\ / / / / / 2 ___\ |
|| / / / | 49*y \/ 3 | / / / / | 49*y \/ 3 | | || / / / | 49*y \/ 3 | / / / / | 49*y \/ 3 | |
|| / / / |- ----- + -----| 8 4 / / / / |- ----- + -----| 8 4 | || / / / |- ----- + -----| 8 4 / / / / |- ----- + -----| 8 4 |
|| / / / \ 25 25 / 5764801*y 2401*y / / / / \ 25 25 / 5764801*y 2401*y | || / / / \ 25 25 / 5764801*y 2401*y / / / / \ 25 25 / 5764801*y 2401*y |
|| / 3*3 / / ------------------ + ---------- + ------- / / 3*3 / / ------------------ + ---------- + ------- | || / 3*3 / / ------------------ + ---------- + ------- / / 3*3 / / ------------------ + ---------- + ------- |
|| \/ \/ \/ 27 100000000 10000 \/ \/ \/ \/ 27 100000000 10000 | || \/ \/ \/ 27 100000000 10000 \/ \/ \/ \/ 27 100000000 10000 |
||- ------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||- ------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 / \\ 2 2 /
$$x_{1} = \operatorname{re}{\left(\begin{cases} - \frac{\sqrt[3]{5} \cdot 7^{\frac{2}{3}} \sqrt{- \sqrt[3]{- y^{4}}}}{10} - \frac{\sqrt{- \frac{14 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} y^{2}}{25 \sqrt{- \sqrt[3]{- y^{4}}}} + \frac{7 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} \sqrt[3]{- y^{4}}}{25}}}{2} & \text{for}\: \frac{49 y^{2}}{25} - \frac{\sqrt{3}}{25} = 0 \\- \frac{\sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} - \frac{\sqrt{- \frac{98 y^{2}}{25 \sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}} + \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} - 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{\sqrt[3]{5} \cdot 7^{\frac{2}{3}} \sqrt{- \sqrt[3]{- y^{4}}}}{10} - \frac{\sqrt{- \frac{14 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} y^{2}}{25 \sqrt{- \sqrt[3]{- y^{4}}}} + \frac{7 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} \sqrt[3]{- y^{4}}}{25}}}{2} & \text{for}\: \frac{49 y^{2}}{25} - \frac{\sqrt{3}}{25} = 0 \\- \frac{\sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} - \frac{\sqrt{- \frac{98 y^{2}}{25 \sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}} + \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} - 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// ____________________________________________ \ // ____________________________________________ \
|| / _____ | || / _____ |
|| / 2/3 3 ___ 3 / 4 2/3 3 ___ 2 | || / 2/3 3 ___ 3 / 4 2/3 3 ___ 2 |
|| / 7*5 *\/ 7 *\/ -y 14*5 *\/ 7 *y | || / 7*5 *\/ 7 *\/ -y 14*5 *\/ 7 *y |
|| / --------------------- - ------------------ | || / --------------------- - ------------------ |
|| / 25 ___________ ___________ | || / 25 ___________ ___________ |
|| / / _____ / _____ | || / / _____ / _____ |
|| / / 3 / 4 3 ___ 2/3 / 3 / 4 ___ 2 | || / / 3 / 4 3 ___ 2/3 / 3 / 4 ___ 2 |
|| \/ 25*\/ -\/ -y \/ 5 *7 *\/ -\/ -y \/ 3 49*y | || \/ 25*\/ -\/ -y \/ 5 *7 *\/ -\/ -y \/ 3 49*y |
|| ----------------------------------------------------- - -------------------------- for - ----- + ----- = 0| || ----------------------------------------------------- - -------------------------- for - ----- + ----- = 0|
|| 2 10 25 25 | || 2 10 25 25 |
|| | || |
|| ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________ | || / _____________________________________________________ |
|| / / _________________________________ | || / / _________________________________ |
|| / / / 3 | || / / / 3 |
|| / / / / 2 ___\ / 2 ___\ | || / / / / 2 ___\ / 2 ___\ |
|| / / / | 49*y \/ 3 | | 49*y \/ 3 | | || / / / | 49*y \/ 3 | | 49*y \/ 3 | |
|| / / / |- ----- + -----| 8 4 2 2*|- ----- + -----| | || / / / |- ----- + -----| 8 4 2 2*|- ----- + -----| |
|| / / / \ 25 25 / 5764801*y 2401*y 98*y \ 25 25 / | || / / / \ 25 25 / 5764801*y 2401*y 98*y \ 25 25 / |
x2 = I*im|< / - 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------- | + re|< / - 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------- |
|| / \/ \/ 27 100000000 10000 _____________________________________________________________________________________________________________________________________ _____________________________________________________ _____________________________________________________________________________________________________________________________________ | || / \/ \/ 27 100000000 10000 _____________________________________________________________________________________________________________________________________ _____________________________________________________ _____________________________________________________________________________________________________________________________________ |
|| / / _____________________________________________________ / _________________________________ / _____________________________________________________ | || / / _____________________________________________________ / _________________________________ / _____________________________________________________ |
|| / / / _________________________________ / / 3 / / _________________________________ | || / / / _________________________________ / / 3 / / _________________________________ |
|| / / / / 3 / / / 2 ___\ / / / 3 | || / / / / 3 / / / 2 ___\ / / / 3 |
|| / / / / / 2 ___\ / 2 ___\ / / | 49*y \/ 3 | / / / / 2 ___\ / 2 ___\ | || / / / / / 2 ___\ / 2 ___\ / / | 49*y \/ 3 | / / / / 2 ___\ / 2 ___\ |
|| / / / / | 49*y \/ 3 | | 49*y \/ 3 | / / |- ----- + -----| 8 4 / / / | 49*y \/ 3 | | 49*y \/ 3 | | || / / / / | 49*y \/ 3 | | 49*y \/ 3 | / / |- ----- + -----| 8 4 / / / | 49*y \/ 3 | | 49*y \/ 3 | |
|| / / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / \ 25 25 / 5764801*y 2401*y / / / |- ----- + -----| 8 4 2*|- ----- + -----| | || / / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / \ 25 25 / 5764801*y 2401*y / / / |- ----- + -----| 8 4 2*|- ----- + -----| |
|| / / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / 3*3 / / ------------------ + ---------- + ------- / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / | || / / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / 3*3 / / ------------------ + ---------- + ------- / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / |
|| / 25* / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- \/ \/ 27 100000000 10000 / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- | || / 25* / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- \/ \/ 27 100000000 10000 / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- |
|| / / \/ \/ 27 100000000 10000 _____________________________________________________ / \/ \/ 27 100000000 10000 _____________________________________________________ | || / / \/ \/ 27 100000000 10000 _____________________________________________________ / \/ \/ 27 100000000 10000 _____________________________________________________ |
|| / / / _________________________________ / / _________________________________ | || / / / _________________________________ / / _________________________________ |
|| / / / / 3 / / / 3 | || / / / / 3 / / / 3 |
|| / / / / / 2 ___\ / / / / 2 ___\ | || / / / / / 2 ___\ / / / / 2 ___\ |
|| / / / / | 49*y \/ 3 | / / / | 49*y \/ 3 | | || / / / / | 49*y \/ 3 | / / / | 49*y \/ 3 | |
|| / / / / |- ----- + -----| 8 4 / / / |- ----- + -----| 8 4 | || / / / / |- ----- + -----| 8 4 / / / |- ----- + -----| 8 4 |
|| / / / / \ 25 25 / 5764801*y 2401*y / / / \ 25 25 / 5764801*y 2401*y | || / / / / \ 25 25 / 5764801*y 2401*y / / / \ 25 25 / 5764801*y 2401*y |
|| / / 3*3 / / ------------------ + ---------- + ------- / 3*3 / / ------------------ + ---------- + ------- | || / / 3*3 / / ------------------ + ---------- + ------- / 3*3 / / ------------------ + ---------- + ------- |
||\/ \/ \/ \/ 27 100000000 10000 \/ \/ \/ 27 100000000 10000 | ||\/ \/ \/ \/ 27 100000000 10000 \/ \/ \/ 27 100000000 10000 |
||------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 / \\ 2 2 /
$$x_{2} = \operatorname{re}{\left(\begin{cases} - \frac{\sqrt[3]{5} \cdot 7^{\frac{2}{3}} \sqrt{- \sqrt[3]{- y^{4}}}}{10} + \frac{\sqrt{- \frac{14 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} y^{2}}{25 \sqrt{- \sqrt[3]{- y^{4}}}} + \frac{7 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} \sqrt[3]{- y^{4}}}{25}}}{2} & \text{for}\: \frac{49 y^{2}}{25} - \frac{\sqrt{3}}{25} = 0 \\- \frac{\sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} + \frac{\sqrt{- \frac{98 y^{2}}{25 \sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}} + \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} - 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{\sqrt[3]{5} \cdot 7^{\frac{2}{3}} \sqrt{- \sqrt[3]{- y^{4}}}}{10} + \frac{\sqrt{- \frac{14 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} y^{2}}{25 \sqrt{- \sqrt[3]{- y^{4}}}} + \frac{7 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} \sqrt[3]{- y^{4}}}{25}}}{2} & \text{for}\: \frac{49 y^{2}}{25} - \frac{\sqrt{3}}{25} = 0 \\- \frac{\sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} + \frac{\sqrt{- \frac{98 y^{2}}{25 \sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}} + \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} - 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// ____________________________________________ \ // ____________________________________________ \
|| / _____ | || / _____ |
|| / 2/3 3 ___ 3 / 4 2/3 3 ___ 2 | || / 2/3 3 ___ 3 / 4 2/3 3 ___ 2 |
|| / 7*5 *\/ 7 *\/ -y 14*5 *\/ 7 *y | || / 7*5 *\/ 7 *\/ -y 14*5 *\/ 7 *y |
|| / --------------------- + ------------------ | || / --------------------- + ------------------ |
|| / 25 ___________ ___________ | || / 25 ___________ ___________ |
|| / / _____ / _____ | || / / _____ / _____ |
|| / / 3 / 4 3 ___ 2/3 / 3 / 4 ___ 2 | || / / 3 / 4 3 ___ 2/3 / 3 / 4 ___ 2 |
|| \/ 25*\/ -\/ -y \/ 5 *7 *\/ -\/ -y \/ 3 49*y | || \/ 25*\/ -\/ -y \/ 5 *7 *\/ -\/ -y \/ 3 49*y |
|| - ----------------------------------------------------- + -------------------------- for - ----- + ----- = 0| || - ----------------------------------------------------- + -------------------------- for - ----- + ----- = 0|
|| 2 10 25 25 | || 2 10 25 25 |
|| | || |
|| ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________ | || / _____________________________________________________ |
|| / / _________________________________ | || / / _________________________________ |
|| / / / 3 | || / / / 3 |
|| / / / / 2 ___\ / 2 ___\ | || / / / / 2 ___\ / 2 ___\ |
|| / / / | 49*y \/ 3 | | 49*y \/ 3 | | || / / / | 49*y \/ 3 | | 49*y \/ 3 | |
|| / / / |- ----- + -----| 8 4 2*|- ----- + -----| 2 | || / / / |- ----- + -----| 8 4 2*|- ----- + -----| 2 |
|| / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / 98*y | || / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / 98*y |
x3 = I*im|< / - 2*3 / / ------------------ + ---------- + ------- + ---------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------- | + re|< / - 2*3 / / ------------------ + ---------- + ------- + ---------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| _____________________________________________________________________________________________________________________________________ / \/ \/ 27 100000000 10000 _____________________________________________________ _____________________________________________________________________________________________________________________________________ | || _____________________________________________________________________________________________________________________________________ / \/ \/ 27 100000000 10000 _____________________________________________________ _____________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________ / / _________________________________ / _____________________________________________________ | || / _____________________________________________________ / / _________________________________ / _____________________________________________________ |
|| / / _________________________________ / / / 3 / / _________________________________ | || / / _________________________________ / / / 3 / / _________________________________ |
|| / / / 3 / / / / 2 ___\ / / / 3 | || / / / 3 / / / / 2 ___\ / / / 3 |
|| / / / / 2 ___\ / 2 ___\ / / / | 49*y \/ 3 | / / / / 2 ___\ / 2 ___\ | || / / / / 2 ___\ / 2 ___\ / / / | 49*y \/ 3 | / / / / 2 ___\ / 2 ___\ |
|| / / / | 49*y \/ 3 | | 49*y \/ 3 | / / / |- ----- + -----| 8 4 / / / | 49*y \/ 3 | | 49*y \/ 3 | | || / / / | 49*y \/ 3 | | 49*y \/ 3 | / / / |- ----- + -----| 8 4 / / / | 49*y \/ 3 | | 49*y \/ 3 | |
|| / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / / \ 25 25 / 5764801*y 2401*y / / / |- ----- + -----| 8 4 2*|- ----- + -----| | || / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / / \ 25 25 / 5764801*y 2401*y / / / |- ----- + -----| 8 4 2*|- ----- + -----| |
|| / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / / 3*3 / / ------------------ + ---------- + ------- / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / | || / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / / 3*3 / / ------------------ + ---------- + ------- / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / |
|| / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- / \/ \/ 27 100000000 10000 25* / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- | || / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- / \/ \/ 27 100000000 10000 25* / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- |
|| / \/ \/ 27 100000000 10000 _____________________________________________________ / / \/ \/ 27 100000000 10000 _____________________________________________________ | || / \/ \/ 27 100000000 10000 _____________________________________________________ / / \/ \/ 27 100000000 10000 _____________________________________________________ |
|| / / _________________________________ / / / _________________________________ | || / / _________________________________ / / / _________________________________ |
|| / / / 3 / / / / 3 | || / / / 3 / / / / 3 |
|| / / / / 2 ___\ / / / / / 2 ___\ | || / / / / 2 ___\ / / / / / 2 ___\ |
|| / / / | 49*y \/ 3 | / / / / | 49*y \/ 3 | | || / / / | 49*y \/ 3 | / / / / | 49*y \/ 3 | |
|| / / / |- ----- + -----| 8 4 / / / / |- ----- + -----| 8 4 | || / / / |- ----- + -----| 8 4 / / / / |- ----- + -----| 8 4 |
|| / / / \ 25 25 / 5764801*y 2401*y / / / / \ 25 25 / 5764801*y 2401*y | || / / / \ 25 25 / 5764801*y 2401*y / / / / \ 25 25 / 5764801*y 2401*y |
|| / 3*3 / / ------------------ + ---------- + ------- / / 3*3 / / ------------------ + ---------- + ------- | || / 3*3 / / ------------------ + ---------- + ------- / / 3*3 / / ------------------ + ---------- + ------- |
||\/ \/ \/ 27 100000000 10000 \/ \/ \/ \/ 27 100000000 10000 | ||\/ \/ \/ 27 100000000 10000 \/ \/ \/ \/ 27 100000000 10000 |
||------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 / \\ 2 2 /
$$x_{3} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt[3]{5} \cdot 7^{\frac{2}{3}} \sqrt{- \sqrt[3]{- y^{4}}}}{10} - \frac{\sqrt{\frac{14 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} y^{2}}{25 \sqrt{- \sqrt[3]{- y^{4}}}} + \frac{7 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} \sqrt[3]{- y^{4}}}{25}}}{2} & \text{for}\: \frac{49 y^{2}}{25} - \frac{\sqrt{3}}{25} = 0 \\\frac{\sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} - \frac{\sqrt{\frac{98 y^{2}}{25 \sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}} + \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} - 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt[3]{5} \cdot 7^{\frac{2}{3}} \sqrt{- \sqrt[3]{- y^{4}}}}{10} - \frac{\sqrt{\frac{14 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} y^{2}}{25 \sqrt{- \sqrt[3]{- y^{4}}}} + \frac{7 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} \sqrt[3]{- y^{4}}}{25}}}{2} & \text{for}\: \frac{49 y^{2}}{25} - \frac{\sqrt{3}}{25} = 0 \\\frac{\sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} - \frac{\sqrt{\frac{98 y^{2}}{25 \sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}} + \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} - 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// ____________________________________________ \ // ____________________________________________ \
|| / _____ | || / _____ |
|| / 2/3 3 ___ 3 / 4 2/3 3 ___ 2 | || / 2/3 3 ___ 3 / 4 2/3 3 ___ 2 |
|| / 7*5 *\/ 7 *\/ -y 14*5 *\/ 7 *y | || / 7*5 *\/ 7 *\/ -y 14*5 *\/ 7 *y |
|| / --------------------- + ------------------ | || / --------------------- + ------------------ |
|| / 25 ___________ ___________ | || / 25 ___________ ___________ |
|| / / _____ / _____ | || / / _____ / _____ |
|| / / 3 / 4 3 ___ 2/3 / 3 / 4 ___ 2 | || / / 3 / 4 3 ___ 2/3 / 3 / 4 ___ 2 |
|| \/ 25*\/ -\/ -y \/ 5 *7 *\/ -\/ -y \/ 3 49*y | || \/ 25*\/ -\/ -y \/ 5 *7 *\/ -\/ -y \/ 3 49*y |
|| ----------------------------------------------------- + -------------------------- for - ----- + ----- = 0| || ----------------------------------------------------- + -------------------------- for - ----- + ----- = 0|
|| 2 10 25 25 | || 2 10 25 25 |
|| | || |
|| ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________ | || / _____________________________________________________ |
|| / / _________________________________ | || / / _________________________________ |
|| / / / 3 | || / / / 3 |
|| / / / / 2 ___\ / 2 ___\ | || / / / / 2 ___\ / 2 ___\ |
|| / / / | 49*y \/ 3 | | 49*y \/ 3 | | || / / / | 49*y \/ 3 | | 49*y \/ 3 | |
|| / / / |- ----- + -----| 8 4 2*|- ----- + -----| 2 | || / / / |- ----- + -----| 8 4 2*|- ----- + -----| 2 |
|| / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / 98*y | || / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / 98*y |
x4 = I*im|< / - 2*3 / / ------------------ + ---------- + ------- + ---------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------- | + re|< / - 2*3 / / ------------------ + ---------- + ------- + ---------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| _____________________________________________________________________________________________________________________________________ / \/ \/ 27 100000000 10000 _____________________________________________________ _____________________________________________________________________________________________________________________________________ | || _____________________________________________________________________________________________________________________________________ / \/ \/ 27 100000000 10000 _____________________________________________________ _____________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________ / / _________________________________ / _____________________________________________________ | || / _____________________________________________________ / / _________________________________ / _____________________________________________________ |
|| / / _________________________________ / / / 3 / / _________________________________ | || / / _________________________________ / / / 3 / / _________________________________ |
|| / / / 3 / / / / 2 ___\ / / / 3 | || / / / 3 / / / / 2 ___\ / / / 3 |
|| / / / / 2 ___\ / 2 ___\ / / / | 49*y \/ 3 | / / / / 2 ___\ / 2 ___\ | || / / / / 2 ___\ / 2 ___\ / / / | 49*y \/ 3 | / / / / 2 ___\ / 2 ___\ |
|| / / / | 49*y \/ 3 | | 49*y \/ 3 | / / / |- ----- + -----| 8 4 / / / | 49*y \/ 3 | | 49*y \/ 3 | | || / / / | 49*y \/ 3 | | 49*y \/ 3 | / / / |- ----- + -----| 8 4 / / / | 49*y \/ 3 | | 49*y \/ 3 | |
|| / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / / \ 25 25 / 5764801*y 2401*y / / / |- ----- + -----| 8 4 2*|- ----- + -----| | || / / / |- ----- + -----| 8 4 2*|- ----- + -----| / / / \ 25 25 / 5764801*y 2401*y / / / |- ----- + -----| 8 4 2*|- ----- + -----| |
|| / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / / 3*3 / / ------------------ + ---------- + ------- / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / | || / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / / 3*3 / / ------------------ + ---------- + ------- / / / \ 25 25 / 5764801*y 2401*y \ 25 25 / |
|| / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- / \/ \/ 27 100000000 10000 25* / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- | || / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- / \/ \/ 27 100000000 10000 25* / 2*3 / / ------------------ + ---------- + ------- - ---------------------------------------------------------------- |
|| / \/ \/ 27 100000000 10000 _____________________________________________________ / / \/ \/ 27 100000000 10000 _____________________________________________________ | || / \/ \/ 27 100000000 10000 _____________________________________________________ / / \/ \/ 27 100000000 10000 _____________________________________________________ |
|| / / _________________________________ / / / _________________________________ | || / / _________________________________ / / / _________________________________ |
|| / / / 3 / / / / 3 | || / / / 3 / / / / 3 |
|| / / / / 2 ___\ / / / / / 2 ___\ | || / / / / 2 ___\ / / / / / 2 ___\ |
|| / / / | 49*y \/ 3 | / / / / | 49*y \/ 3 | | || / / / | 49*y \/ 3 | / / / / | 49*y \/ 3 | |
|| / / / |- ----- + -----| 8 4 / / / / |- ----- + -----| 8 4 | || / / / |- ----- + -----| 8 4 / / / / |- ----- + -----| 8 4 |
|| / / / \ 25 25 / 5764801*y 2401*y / / / / \ 25 25 / 5764801*y 2401*y | || / / / \ 25 25 / 5764801*y 2401*y / / / / \ 25 25 / 5764801*y 2401*y |
|| / 3*3 / / ------------------ + ---------- + ------- / / 3*3 / / ------------------ + ---------- + ------- | || / 3*3 / / ------------------ + ---------- + ------- / / 3*3 / / ------------------ + ---------- + ------- |
||\/ \/ \/ 27 100000000 10000 \/ \/ \/ \/ 27 100000000 10000 | ||\/ \/ \/ 27 100000000 10000 \/ \/ \/ \/ 27 100000000 10000 |
||------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 / \\ 2 2 /
$$x_{4} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt[3]{5} \cdot 7^{\frac{2}{3}} \sqrt{- \sqrt[3]{- y^{4}}}}{10} + \frac{\sqrt{\frac{14 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} y^{2}}{25 \sqrt{- \sqrt[3]{- y^{4}}}} + \frac{7 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} \sqrt[3]{- y^{4}}}{25}}}{2} & \text{for}\: \frac{49 y^{2}}{25} - \frac{\sqrt{3}}{25} = 0 \\\frac{\sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} + \frac{\sqrt{\frac{98 y^{2}}{25 \sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}} + \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} - 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt[3]{5} \cdot 7^{\frac{2}{3}} \sqrt{- \sqrt[3]{- y^{4}}}}{10} + \frac{\sqrt{\frac{14 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} y^{2}}{25 \sqrt{- \sqrt[3]{- y^{4}}}} + \frac{7 \cdot 5^{\frac{2}{3}} \sqrt[3]{7} \sqrt[3]{- y^{4}}}{25}}}{2} & \text{for}\: \frac{49 y^{2}}{25} - \frac{\sqrt{3}}{25} = 0 \\\frac{\sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} + \frac{\sqrt{\frac{98 y^{2}}{25 \sqrt{- \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} + 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}} + \frac{2 \left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)}{3 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}} - 2 \sqrt[3]{\frac{2401 y^{4}}{10000} + \sqrt{\frac{5764801 y^{8}}{100000000} + \frac{\left(- \frac{49 y^{2}}{25} + \frac{\sqrt{3}}{25}\right)^{3}}{27}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((5^(1/3)*7^(2/3)*sqrt(-(-y^4)^(1/3))/10 + sqrt(14*5^(2/3)*7^(1/3)*y^2/(25*sqrt(-(-y^4)^(1/3))) + 7*5^(2/3)*7^(1/3)*(-y^4)^(1/3)/25/2, 49*y^2/25 - sqrt(3)/25 = 0), (sqrt(-2*(-49*y^2/25 + sqrt(3)/25)/(3*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3)) + 2*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3))/2 + sqrt(98*y^2/(25*sqrt(-2*(-49*y^2/25 + sqrt(3)/25)/(3*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3)) + 2*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3))) + 2*(-49*y^2/25 + sqrt(3)/25)/(3*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3)) - 2*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3))/2, True))) + i*im(Piecewise((5^(1/3)*7^(2/3)*sqrt(-(-y^4)^(1/3))/10 + sqrt(14*5^(2/3)*7^(1/3)*y^2/(25*sqrt(-(-y^4)^(1/3))) + 7*5^(2/3)*7^(1/3)*(-y^4)^(1/3)/25)/2, 49*y^2/25 - sqrt(3)/25 = 0), (sqrt(-2*(-49*y^2/25 + sqrt(3)/25)/(3*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3)) + 2*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3))/2 + sqrt(98*y^2/(25*sqrt(-2*(-49*y^2/25 + sqrt(3)/25)/(3*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3)) + 2*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3))) + 2*(-49*y^2/25 + sqrt(3)/25)/(3*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3)) - 2*(2401*y^4/10000 + sqrt(5764801*y^8/100000000 + (-49*y^2/25 + sqrt(3)/25)^3/27))^(1/3))/2, True))))