find the value of y

4x^2 - y^3 = 5xy^2

asked by guest
on Nov 25, 2024 at 5:26 am



You asked:

Solve the equation \[4 {x}^{2} - {y}^{3} = 5 x \cdot {y}^{2}\] for the unknown \(y\).

MathBot Answer:

$$\begin{aligned}y &= - \frac{25 x^{2}}{3 \sqrt[3]{125 x^{3} - 54 x^{2} + \frac{\sqrt{- 62500 x^{6} + \left(250 x^{3} - 108 x^{2}\right)^{2}}}{2}}} - \frac{5 x}{3} - \frac{\sqrt[3]{125 x^{3} - 54 x^{2} + \frac{\sqrt{- 62500 x^{6} + \left(250 x^{3} - 108 x^{2}\right)^{2}}}{2}}}{3}\\y &= - \frac{25 x^{2}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 x^{3} - 54 x^{2} + \frac{\sqrt{- 62500 x^{6} + \left(250 x^{3} - 108 x^{2}\right)^{2}}}{2}}} - \frac{5 x}{3} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 x^{3} - 54 x^{2} + \frac{\sqrt{- 62500 x^{6} + \left(250 x^{3} - 108 x^{2}\right)^{2}}}{2}}}{3}\\y &= - \frac{25 x^{2}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 x^{3} - 54 x^{2} + \frac{\sqrt{- 62500 x^{6} + \left(250 x^{3} - 108 x^{2}\right)^{2}}}{2}}} - \frac{5 x}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 x^{3} - 54 x^{2} + \frac{\sqrt{- 62500 x^{6} + \left(250 x^{3} - 108 x^{2}\right)^{2}}}{2}}}{3}\end{aligned}$$

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