x+(70/x^2)=7.7

asked by guest
on Jan 16, 2025 at 2:41 am



You asked:

Solve the equation \(x + \frac{70}{{x}^{2}} = 7.7\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= \frac{77}{30} - \frac{5929}{300 \sqrt[3]{\frac{488467}{1000} + \frac{21 \sqrt{6843}}{10}}} - \frac{\sqrt[3]{\frac{488467}{1000} + \frac{21 \sqrt{6843}}{10}}}{3} \approx -2.6061574\\x &= \frac{5929}{600 \sqrt[3]{\frac{21 \sqrt{6843}}{10} + \frac{488467}{1000}}} + \frac{\sqrt[3]{\frac{21 \sqrt{6843}}{10} + \frac{488467}{1000}}}{6} + \frac{77}{30} + i \left(- \frac{5929 \sqrt{3}}{600 \sqrt[3]{\frac{21 \sqrt{6843}}{10} + \frac{488467}{1000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{21 \sqrt{6843}}{10} + \frac{488467}{1000}}}{6}\right) \approx 5.1530787 + 0.55249253 i\\x &= \frac{5929}{600 \sqrt[3]{\frac{21 \sqrt{6843}}{10} + \frac{488467}{1000}}} + \frac{\sqrt[3]{\frac{21 \sqrt{6843}}{10} + \frac{488467}{1000}}}{6} + \frac{77}{30} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{21 \sqrt{6843}}{10} + \frac{488467}{1000}}}{6} + \frac{5929 \sqrt{3}}{600 \sqrt[3]{\frac{21 \sqrt{6843}}{10} + \frac{488467}{1000}}}\right) \approx 5.1530787 -0.55249253 i\end{aligned}\]

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

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