2=x- $\frac{2\}{x^2}$

asked by guest
on Nov 29, 2024 at 9:25 am



You asked:

Solve the equation \(2 = x - \frac{2}{{x}^{2}}\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= \frac{2}{3} + \sqrt[3]{\frac{35}{27} + \frac{\sqrt{129}}{9}} + \frac{4}{9 \sqrt[3]{\frac{35}{27} + \frac{\sqrt{129}}{9}}} \approx 2.3593041\\x &= - \frac{\sqrt[3]{\frac{\sqrt{129}}{9} + \frac{35}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{129}}{9} + \frac{35}{27}}} + \frac{2}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{129}}{9} + \frac{35}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{129}}{9} + \frac{35}{27}}}{2}\right) \approx -0.17965204 + 0.90301315 i\\x &= - \frac{\sqrt[3]{\frac{\sqrt{129}}{9} + \frac{35}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{129}}{9} + \frac{35}{27}}} + \frac{2}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{129}}{9} + \frac{35}{27}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{129}}{9} + \frac{35}{27}}}\right) \approx -0.17965204 -0.90301315 i\end{aligned}\]

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

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