$60x^{3}$ - 24x + 10 = 0

asked by guest
on Nov 24, 2024 at 6:11 pm



You asked:

Solve the equation \(60 {x}^{3} - 24 x + 10 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{2}{5 \sqrt[3]{\frac{9}{4} + \frac{3 \sqrt{3705}}{100}}} - \frac{\sqrt[3]{\frac{9}{4} + \frac{3 \sqrt{3705}}{100}}}{3} \approx -0.78287351\\x &= \frac{1}{5 \sqrt[3]{\frac{3 \sqrt{3705}}{100} + \frac{9}{4}}} + \frac{\sqrt[3]{\frac{3 \sqrt{3705}}{100} + \frac{9}{4}}}{6} + i \left(- \frac{\sqrt{3}}{5 \sqrt[3]{\frac{3 \sqrt{3705}}{100} + \frac{9}{4}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{3705}}{100} + \frac{9}{4}}}{6}\right) \approx 0.39143675 + 0.24427074 i\\x &= \frac{1}{5 \sqrt[3]{\frac{3 \sqrt{3705}}{100} + \frac{9}{4}}} + \frac{\sqrt[3]{\frac{3 \sqrt{3705}}{100} + \frac{9}{4}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{3705}}{100} + \frac{9}{4}}}{6} + \frac{\sqrt{3}}{5 \sqrt[3]{\frac{3 \sqrt{3705}}{100} + \frac{9}{4}}}\right) \approx 0.39143675 -0.24427074 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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