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(-5)*x^4*y-3*7*x-2*y-6=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 -5*x *y - 21*x - 2*y - 6 = 0
$$\left(- 2 y + \left(- 21 x + - 5 x^{4} y\right)\right) - 6 = 0$$
Gráfica
Respuesta rápida
[src]
// __________________________________________________ \ // __________________________________________________ \
|| / _____ | || / _____ |
|| / 3 ___ 2/3 / -1 | || / 3 ___ 2/3 / -1 |
|| / \/ 5 *21 * / --- | || / \/ 5 *21 * / --- |
|| / 3 / 2 3 ___ 2/3 | || / 3 / 2 3 ___ 2/3 |
|| / \/ y 2*\/ 5 *21 | || / \/ y 2*\/ 5 *21 |
|| / ---------------------- + ----------------------- | || / ---------------------- + ----------------------- |
|| / 5 _____________ _____________ | || / 5 _____________ _____________ |
|| / / _____ / _____ | || / / _____ / _____ |
|| / / / -1 2/3 3 ____ / / -1 | || / / / -1 2/3 3 ____ / / -1 |
|| / 5*y* / - / --- 5 *\/ 21 * / - / --- | || / 5*y* / - / --- 5 *\/ 21 * / - / --- |
|| / / 3 / 2 / 3 / 2 | || / / 3 / 2 / 3 / 2 |
|| \/ \/ \/ y \/ \/ y 6 + 2*y | || \/ \/ \/ y \/ \/ y 6 + 2*y |
|| - --------------------------------------------------------------- - ------------------------------- for ------- = 0| || - --------------------------------------------------------------- - ------------------------------- for ------- = 0|
|| 2 10 5*y | || 2 10 5*y |
|| | || |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _________________________________________ | || / _________________________________________ |
x1 = I*im|< / / ________________________ | + re|< / / ________________________ |
|| / / / 3 | || / / / 3 |
|| / / / 194481 (6 + 2*y) 441 42 2*(6 + 2*y) | || / / / 194481 (6 + 2*y) 441 42 2*(6 + 2*y) |
|| / - 2* / / --------- - ---------- + ------ + ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- | || / - 2* / / --------- - ---------- + ------ + ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- |
|| ____________________________________________________________________________________________________________ / 3 / / 4 3 2 ____________________________________________________________________________________________________________ _________________________________________ | || ____________________________________________________________________________________________________________ / 3 / / 4 3 2 ____________________________________________________________________________________________________________ _________________________________________ |
|| / _________________________________________ / \/ \/ 160000*y 3375*y 400*y / _________________________________________ / ________________________ | || / _________________________________________ / \/ \/ 160000*y 3375*y 400*y / _________________________________________ / ________________________ |
|| / / ________________________ / / / ________________________ / / 3 | || / / ________________________ / / / ________________________ / / 3 |
|| / / / 3 / / / / 3 / / 194481 (6 + 2*y) 441 | || / / / 3 / / / / 3 / / 194481 (6 + 2*y) 441 |
|| / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) / / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) 15*y* / / --------- - ---------- + ------ | || / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) / / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) 15*y* / / --------- - ---------- + ------ |
|| / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- / 5*y* / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- 3 / / 4 3 2 | || / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- / 5*y* / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- 3 / / 4 3 2 |
|| / 3 / / 4 3 2 _________________________________________ / / 3 / / 4 3 2 _________________________________________ \/ \/ 160000*y 3375*y 400*y | || / 3 / / 4 3 2 _________________________________________ / / 3 / / 4 3 2 _________________________________________ \/ \/ 160000*y 3375*y 400*y |
|| / \/ \/ 160000*y 3375*y 400*y / ________________________ / / \/ \/ 160000*y 3375*y 400*y / ________________________ | || / \/ \/ 160000*y 3375*y 400*y / ________________________ / / \/ \/ 160000*y 3375*y 400*y / ________________________ |
|| / / / 3 / / / / 3 | || / / / 3 / / / / 3 |
|| / / / 194481 (6 + 2*y) 441 / / / / 194481 (6 + 2*y) 441 | || / / / 194481 (6 + 2*y) 441 / / / / 194481 (6 + 2*y) 441 |
|| / 15*y* / / --------- - ---------- + ------ / / 15*y* / / --------- - ---------- + ------ | || / 15*y* / / --------- - ---------- + ------ / / 15*y* / / --------- - ---------- + ------ |
|| / 3 / / 4 3 2 / / 3 / / 4 3 2 | || / 3 / / 4 3 2 / / 3 / / 4 3 2 |
|| \/ \/ \/ 160000*y 3375*y 400*y \/ \/ \/ \/ 160000*y 3375*y 400*y | || \/ \/ \/ 160000*y 3375*y 400*y \/ \/ \/ \/ 160000*y 3375*y 400*y |
||- ------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||- ------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 / \\ 2 2 /
$$x_{1} = \operatorname{re}{\left(\begin{cases} - \frac{\sqrt[3]{21} \cdot 5^{\frac{2}{3}} \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}{10} - \frac{\sqrt{\frac{21^{\frac{2}{3}} \sqrt[3]{5} \sqrt[3]{- \frac{1}{y^{2}}}}{5} + \frac{2 \cdot 21^{\frac{2}{3}} \sqrt[3]{5}}{5 y \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}}}{2} & \text{for}\: \frac{2 y + 6}{5 y} = 0 \\- \frac{\sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} - \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}} + \frac{42}{5 y \sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{\sqrt[3]{21} \cdot 5^{\frac{2}{3}} \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}{10} - \frac{\sqrt{\frac{21^{\frac{2}{3}} \sqrt[3]{5} \sqrt[3]{- \frac{1}{y^{2}}}}{5} + \frac{2 \cdot 21^{\frac{2}{3}} \sqrt[3]{5}}{5 y \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}}}{2} & \text{for}\: \frac{2 y + 6}{5 y} = 0 \\- \frac{\sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} - \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}} + \frac{42}{5 y \sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// __________________________________________________ \ // __________________________________________________ \
|| / _____ | || / _____ |
|| / 3 ___ 2/3 / -1 | || / 3 ___ 2/3 / -1 |
|| / \/ 5 *21 * / --- | || / \/ 5 *21 * / --- |
|| / 3 / 2 3 ___ 2/3 | || / 3 / 2 3 ___ 2/3 |
|| / \/ y 2*\/ 5 *21 | || / \/ y 2*\/ 5 *21 |
|| / ---------------------- + ----------------------- | || / ---------------------- + ----------------------- |
|| / 5 _____________ _____________ | || / 5 _____________ _____________ |
|| / / _____ / _____ | || / / _____ / _____ |
|| / / / -1 2/3 3 ____ / / -1 | || / / / -1 2/3 3 ____ / / -1 |
|| / 5*y* / - / --- 5 *\/ 21 * / - / --- | || / 5*y* / - / --- 5 *\/ 21 * / - / --- |
|| / / 3 / 2 / 3 / 2 | || / / 3 / 2 / 3 / 2 |
|| \/ \/ \/ y \/ \/ y 6 + 2*y | || \/ \/ \/ y \/ \/ y 6 + 2*y |
|| --------------------------------------------------------------- - ------------------------------- for ------- = 0| || --------------------------------------------------------------- - ------------------------------- for ------- = 0|
|| 2 10 5*y | || 2 10 5*y |
|| | || |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _________________________________________ | || / _________________________________________ |
x2 = I*im|< / / ________________________ | + re|< / / ________________________ |
|| / / / 3 | || / / / 3 |
|| / / / 194481 (6 + 2*y) 441 42 2*(6 + 2*y) | || / / / 194481 (6 + 2*y) 441 42 2*(6 + 2*y) |
|| / - 2* / / --------- - ---------- + ------ + ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- | || / - 2* / / --------- - ---------- + ------ + ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- |
|| / 3 / / 4 3 2 ____________________________________________________________________________________________________________ _________________________________________ ____________________________________________________________________________________________________________ | || / 3 / / 4 3 2 ____________________________________________________________________________________________________________ _________________________________________ ____________________________________________________________________________________________________________ |
|| / \/ \/ 160000*y 3375*y 400*y / _________________________________________ / ________________________ / _________________________________________ | || / \/ \/ 160000*y 3375*y 400*y / _________________________________________ / ________________________ / _________________________________________ |
|| / / / ________________________ / / 3 / / ________________________ | || / / / ________________________ / / 3 / / ________________________ |
|| / / / / 3 / / 194481 (6 + 2*y) 441 / / / 3 | || / / / / 3 / / 194481 (6 + 2*y) 441 / / / 3 |
|| / / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) 15*y* / / --------- - ---------- + ------ / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) | || / / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) 15*y* / / --------- - ---------- + ------ / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) |
|| / 5*y* / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- 3 / / 4 3 2 / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- | || / 5*y* / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- 3 / / 4 3 2 / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- |
|| / / 3 / / 4 3 2 _________________________________________ \/ \/ 160000*y 3375*y 400*y / 3 / / 4 3 2 _________________________________________ | || / / 3 / / 4 3 2 _________________________________________ \/ \/ 160000*y 3375*y 400*y / 3 / / 4 3 2 _________________________________________ |
|| / / \/ \/ 160000*y 3375*y 400*y / ________________________ / \/ \/ 160000*y 3375*y 400*y / ________________________ | || / / \/ \/ 160000*y 3375*y 400*y / ________________________ / \/ \/ 160000*y 3375*y 400*y / ________________________ |
|| / / / / 3 / / / 3 | || / / / / 3 / / / 3 |
|| / / / / 194481 (6 + 2*y) 441 / / / 194481 (6 + 2*y) 441 | || / / / / 194481 (6 + 2*y) 441 / / / 194481 (6 + 2*y) 441 |
|| / / 15*y* / / --------- - ---------- + ------ / 15*y* / / --------- - ---------- + ------ | || / / 15*y* / / --------- - ---------- + ------ / 15*y* / / --------- - ---------- + ------ |
|| / / 3 / / 4 3 2 / 3 / / 4 3 2 | || / / 3 / / 4 3 2 / 3 / / 4 3 2 |
||\/ \/ \/ \/ 160000*y 3375*y 400*y \/ \/ \/ 160000*y 3375*y 400*y | ||\/ \/ \/ \/ 160000*y 3375*y 400*y \/ \/ \/ 160000*y 3375*y 400*y |
||----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------- otherwise | ||----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 / \\ 2 2 /
$$x_{2} = \operatorname{re}{\left(\begin{cases} - \frac{\sqrt[3]{21} \cdot 5^{\frac{2}{3}} \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}{10} + \frac{\sqrt{\frac{21^{\frac{2}{3}} \sqrt[3]{5} \sqrt[3]{- \frac{1}{y^{2}}}}{5} + \frac{2 \cdot 21^{\frac{2}{3}} \sqrt[3]{5}}{5 y \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}}}{2} & \text{for}\: \frac{2 y + 6}{5 y} = 0 \\- \frac{\sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} - \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}} + \frac{42}{5 y \sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{\sqrt[3]{21} \cdot 5^{\frac{2}{3}} \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}{10} + \frac{\sqrt{\frac{21^{\frac{2}{3}} \sqrt[3]{5} \sqrt[3]{- \frac{1}{y^{2}}}}{5} + \frac{2 \cdot 21^{\frac{2}{3}} \sqrt[3]{5}}{5 y \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}}}{2} & \text{for}\: \frac{2 y + 6}{5 y} = 0 \\- \frac{\sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} - \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}} + \frac{42}{5 y \sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// __________________________________________________ \ // __________________________________________________ \
|| / _____ | || / _____ |
|| / 3 ___ 2/3 / -1 | || / 3 ___ 2/3 / -1 |
|| / \/ 5 *21 * / --- | || / \/ 5 *21 * / --- |
|| / 3 / 2 3 ___ 2/3 | || / 3 / 2 3 ___ 2/3 |
|| / \/ y 2*\/ 5 *21 | || / \/ y 2*\/ 5 *21 |
|| / ---------------------- - ----------------------- | || / ---------------------- - ----------------------- |
|| / 5 _____________ _____________ | || / 5 _____________ _____________ |
|| / / _____ / _____ | || / / _____ / _____ |
|| / / / -1 2/3 3 ____ / / -1 | || / / / -1 2/3 3 ____ / / -1 |
|| / 5*y* / - / --- 5 *\/ 21 * / - / --- | || / 5*y* / - / --- 5 *\/ 21 * / - / --- |
|| / / 3 / 2 / 3 / 2 | || / / 3 / 2 / 3 / 2 |
|| \/ \/ \/ y \/ \/ y 6 + 2*y | || \/ \/ \/ y \/ \/ y 6 + 2*y |
|| - --------------------------------------------------------------- + ------------------------------- for ------- = 0| || - --------------------------------------------------------------- + ------------------------------- for ------- = 0|
|| 2 10 5*y | || 2 10 5*y |
|| | || |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _________________________________________ | || / _________________________________________ |
x3 = I*im|< / / ________________________ | + re|< / / ________________________ |
|| / / / 3 | || / / / 3 |
|| / / / 194481 (6 + 2*y) 441 42 2*(6 + 2*y) | || / / / 194481 (6 + 2*y) 441 42 2*(6 + 2*y) |
|| / - 2* / / --------- - ---------- + ------ - ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- | || / - 2* / / --------- - ---------- + ------ - ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- |
|| ____________________________________________________________________________________________________________ / 3 / / 4 3 2 ____________________________________________________________________________________________________________ _________________________________________ | || ____________________________________________________________________________________________________________ / 3 / / 4 3 2 ____________________________________________________________________________________________________________ _________________________________________ |
|| / _________________________________________ / \/ \/ 160000*y 3375*y 400*y / _________________________________________ / ________________________ | || / _________________________________________ / \/ \/ 160000*y 3375*y 400*y / _________________________________________ / ________________________ |
|| / / ________________________ / / / ________________________ / / 3 | || / / ________________________ / / / ________________________ / / 3 |
|| / / / 3 / / / / 3 / / 194481 (6 + 2*y) 441 | || / / / 3 / / / / 3 / / 194481 (6 + 2*y) 441 |
|| / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) / / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) 15*y* / / --------- - ---------- + ------ | || / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) / / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) 15*y* / / --------- - ---------- + ------ |
|| / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- / 5*y* / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- 3 / / 4 3 2 | || / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- / 5*y* / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- 3 / / 4 3 2 |
|| / 3 / / 4 3 2 _________________________________________ / / 3 / / 4 3 2 _________________________________________ \/ \/ 160000*y 3375*y 400*y | || / 3 / / 4 3 2 _________________________________________ / / 3 / / 4 3 2 _________________________________________ \/ \/ 160000*y 3375*y 400*y |
|| / \/ \/ 160000*y 3375*y 400*y / ________________________ / / \/ \/ 160000*y 3375*y 400*y / ________________________ | || / \/ \/ 160000*y 3375*y 400*y / ________________________ / / \/ \/ 160000*y 3375*y 400*y / ________________________ |
|| / / / 3 / / / / 3 | || / / / 3 / / / / 3 |
|| / / / 194481 (6 + 2*y) 441 / / / / 194481 (6 + 2*y) 441 | || / / / 194481 (6 + 2*y) 441 / / / / 194481 (6 + 2*y) 441 |
|| / 15*y* / / --------- - ---------- + ------ / / 15*y* / / --------- - ---------- + ------ | || / 15*y* / / --------- - ---------- + ------ / / 15*y* / / --------- - ---------- + ------ |
|| / 3 / / 4 3 2 / / 3 / / 4 3 2 | || / 3 / / 4 3 2 / / 3 / / 4 3 2 |
||\/ \/ \/ 160000*y 3375*y 400*y \/ \/ \/ \/ 160000*y 3375*y 400*y | ||\/ \/ \/ 160000*y 3375*y 400*y \/ \/ \/ \/ 160000*y 3375*y 400*y |
||------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 / \\ 2 2 /
$$x_{3} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt[3]{21} \cdot 5^{\frac{2}{3}} \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}{10} - \frac{\sqrt{\frac{21^{\frac{2}{3}} \sqrt[3]{5} \sqrt[3]{- \frac{1}{y^{2}}}}{5} - \frac{2 \cdot 21^{\frac{2}{3}} \sqrt[3]{5}}{5 y \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}}}{2} & \text{for}\: \frac{2 y + 6}{5 y} = 0 \\\frac{\sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} - \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}} - \frac{42}{5 y \sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt[3]{21} \cdot 5^{\frac{2}{3}} \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}{10} - \frac{\sqrt{\frac{21^{\frac{2}{3}} \sqrt[3]{5} \sqrt[3]{- \frac{1}{y^{2}}}}{5} - \frac{2 \cdot 21^{\frac{2}{3}} \sqrt[3]{5}}{5 y \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}}}{2} & \text{for}\: \frac{2 y + 6}{5 y} = 0 \\\frac{\sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} - \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}} - \frac{42}{5 y \sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// __________________________________________________ \ // __________________________________________________ \
|| / _____ | || / _____ |
|| / 3 ___ 2/3 / -1 | || / 3 ___ 2/3 / -1 |
|| / \/ 5 *21 * / --- | || / \/ 5 *21 * / --- |
|| / 3 / 2 3 ___ 2/3 | || / 3 / 2 3 ___ 2/3 |
|| / \/ y 2*\/ 5 *21 | || / \/ y 2*\/ 5 *21 |
|| / ---------------------- - ----------------------- | || / ---------------------- - ----------------------- |
|| / 5 _____________ _____________ | || / 5 _____________ _____________ |
|| / / _____ / _____ | || / / _____ / _____ |
|| / / / -1 2/3 3 ____ / / -1 | || / / / -1 2/3 3 ____ / / -1 |
|| / 5*y* / - / --- 5 *\/ 21 * / - / --- | || / 5*y* / - / --- 5 *\/ 21 * / - / --- |
|| / / 3 / 2 / 3 / 2 | || / / 3 / 2 / 3 / 2 |
|| \/ \/ \/ y \/ \/ y 6 + 2*y | || \/ \/ \/ y \/ \/ y 6 + 2*y |
|| --------------------------------------------------------------- + ------------------------------- for ------- = 0| || --------------------------------------------------------------- + ------------------------------- for ------- = 0|
|| 2 10 5*y | || 2 10 5*y |
|| | || |
|| ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _________________________________________ | || / _________________________________________ |
x4 = I*im|< / / ________________________ | + re|< / / ________________________ |
|| / / / 3 | || / / / 3 |
|| / / / 194481 (6 + 2*y) 441 42 2*(6 + 2*y) | || / / / 194481 (6 + 2*y) 441 42 2*(6 + 2*y) |
|| / - 2* / / --------- - ---------- + ------ - ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- | || / - 2* / / --------- - ---------- + ------ - ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- |
|| ____________________________________________________________________________________________________________ / 3 / / 4 3 2 ____________________________________________________________________________________________________________ _________________________________________ | || ____________________________________________________________________________________________________________ / 3 / / 4 3 2 ____________________________________________________________________________________________________________ _________________________________________ |
|| / _________________________________________ / \/ \/ 160000*y 3375*y 400*y / _________________________________________ / ________________________ | || / _________________________________________ / \/ \/ 160000*y 3375*y 400*y / _________________________________________ / ________________________ |
|| / / ________________________ / / / ________________________ / / 3 | || / / ________________________ / / / ________________________ / / 3 |
|| / / / 3 / / / / 3 / / 194481 (6 + 2*y) 441 | || / / / 3 / / / / 3 / / 194481 (6 + 2*y) 441 |
|| / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) / / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) 15*y* / / --------- - ---------- + ------ | || / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) / / / / 194481 (6 + 2*y) 441 2*(6 + 2*y) 15*y* / / --------- - ---------- + ------ |
|| / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- / 5*y* / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- 3 / / 4 3 2 | || / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- / 5*y* / 2* / / --------- - ---------- + ------ + ----------------------------------------------------- 3 / / 4 3 2 |
|| / 3 / / 4 3 2 _________________________________________ / / 3 / / 4 3 2 _________________________________________ \/ \/ 160000*y 3375*y 400*y | || / 3 / / 4 3 2 _________________________________________ / / 3 / / 4 3 2 _________________________________________ \/ \/ 160000*y 3375*y 400*y |
|| / \/ \/ 160000*y 3375*y 400*y / ________________________ / / \/ \/ 160000*y 3375*y 400*y / ________________________ | || / \/ \/ 160000*y 3375*y 400*y / ________________________ / / \/ \/ 160000*y 3375*y 400*y / ________________________ |
|| / / / 3 / / / / 3 | || / / / 3 / / / / 3 |
|| / / / 194481 (6 + 2*y) 441 / / / / 194481 (6 + 2*y) 441 | || / / / 194481 (6 + 2*y) 441 / / / / 194481 (6 + 2*y) 441 |
|| / 15*y* / / --------- - ---------- + ------ / / 15*y* / / --------- - ---------- + ------ | || / 15*y* / / --------- - ---------- + ------ / / 15*y* / / --------- - ---------- + ------ |
|| / 3 / / 4 3 2 / / 3 / / 4 3 2 | || / 3 / / 4 3 2 / / 3 / / 4 3 2 |
||\/ \/ \/ 160000*y 3375*y 400*y \/ \/ \/ \/ 160000*y 3375*y 400*y | ||\/ \/ \/ 160000*y 3375*y 400*y \/ \/ \/ \/ 160000*y 3375*y 400*y |
||------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 / \\ 2 2 /
$$x_{4} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt[3]{21} \cdot 5^{\frac{2}{3}} \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}{10} + \frac{\sqrt{\frac{21^{\frac{2}{3}} \sqrt[3]{5} \sqrt[3]{- \frac{1}{y^{2}}}}{5} - \frac{2 \cdot 21^{\frac{2}{3}} \sqrt[3]{5}}{5 y \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}}}{2} & \text{for}\: \frac{2 y + 6}{5 y} = 0 \\\frac{\sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} - \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}} - \frac{42}{5 y \sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt[3]{21} \cdot 5^{\frac{2}{3}} \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}{10} + \frac{\sqrt{\frac{21^{\frac{2}{3}} \sqrt[3]{5} \sqrt[3]{- \frac{1}{y^{2}}}}{5} - \frac{2 \cdot 21^{\frac{2}{3}} \sqrt[3]{5}}{5 y \sqrt{- \sqrt[3]{- \frac{1}{y^{2}}}}}}}{2} & \text{for}\: \frac{2 y + 6}{5 y} = 0 \\\frac{\sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} - \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}} - \frac{42}{5 y \sqrt{2 \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}} + \frac{2 \left(2 y + 6\right)}{15 y \sqrt[3]{\sqrt{- \frac{\left(2 y + 6\right)^{3}}{3375 y^{3}} + \frac{194481}{160000 y^{4}}} + \frac{441}{400 y^{2}}}}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((21^(1/3)*5^(2/3)*sqrt(-(-1/y^2)^(1/3))/10 + sqrt(21^(2/3)*5^(1/3)*(-1/y^2)^(1/3)/5 - 2*21^(2/3)*5^(1/3)/(5*y*sqrt(-(-1/y^2)^(1/3)))/2, (2*y + 6)/(5*y) = 0), (sqrt(2*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3) + 2*(2*y + 6)/(15*y*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3)))/2 + sqrt(-2*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3) - 2*(2*y + 6)/(15*y*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3)) - 42/(5*y*sqrt(2*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3) + 2*(2*y + 6)/(15*y*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3)))))/2, True))) + i*im(Piecewise((21^(1/3)*5^(2/3)*sqrt(-(-1/y^2)^(1/3))/10 + sqrt(21^(2/3)*5^(1/3)*(-1/y^2)^(1/3)/5 - 2*21^(2/3)*5^(1/3)/(5*y*sqrt(-(-1/y^2)^(1/3))))/2, (2*y + 6)/(5*y) = 0), (sqrt(2*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3) + 2*(2*y + 6)/(15*y*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3)))/2 + sqrt(-2*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3) - 2*(2*y + 6)/(15*y*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3)) - 42/(5*y*sqrt(2*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3) + 2*(2*y + 6)/(15*y*(sqrt(-(2*y + 6)^3/(3375*y^3) + 194481/(160000*y^4)) + 441/(400*y^2))^(1/3)))))/2, True))))