1/x^2-5x = x+7/x -1

asked by guest
on Jan 19, 2025 at 2:18 am



You asked:

Solve the equation \(\frac{1}{{x}^{2}} - 5 x = x + \frac{7}{x} - 1\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= \frac{1}{18} + \sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}} - \frac{125}{324 \sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}}} \approx 0.1432688\\x &= - \frac{\sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}}}{2} + \frac{1}{18} + \frac{125}{648 \sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}}} + i \left(\frac{125 \sqrt{3}}{648 \sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}}} + \frac{\sqrt{3} \sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}}}{2}\right) \approx 0.011698935 + 1.0785071 i\\x &= - \frac{\sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}}}{2} + \frac{1}{18} + \frac{125}{648 \sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}}}{2} - \frac{125 \sqrt{3}}{648 \sqrt[3]{\frac{149}{2916} + \frac{\sqrt{2801}}{216}}}\right) \approx 0.011698935 -1.0785071 i\end{aligned}\]

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

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