55x²-5x+1/x-5=0

asked by guest
on Nov 17, 2024 at 11:46 pm



You asked:

Solve the equation \(55 \cdot {x}^{2} - 5 x + \frac{1}{x} - 5 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= \frac{1}{33} - \frac{34}{363 \sqrt[3]{\frac{1381}{6655} + \frac{3 \sqrt{849}}{605}}} - \frac{\sqrt[3]{\frac{1381}{6655} + \frac{3 \sqrt{849}}{605}}}{3} \approx -0.33770859\\x &= \frac{1}{33} + \frac{17}{363 \sqrt[3]{\frac{3 \sqrt{849}}{605} + \frac{1381}{6655}}} + \frac{\sqrt[3]{\frac{3 \sqrt{849}}{605} + \frac{1381}{6655}}}{6} + i \left(- \frac{17 \sqrt{3}}{363 \sqrt[3]{\frac{3 \sqrt{849}}{605} + \frac{1381}{6655}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{849}}{605} + \frac{1381}{6655}}}{6}\right) \approx 0.21430884 + 0.088940998 i\\x &= \frac{1}{33} + \frac{17}{363 \sqrt[3]{\frac{3 \sqrt{849}}{605} + \frac{1381}{6655}}} + \frac{\sqrt[3]{\frac{3 \sqrt{849}}{605} + \frac{1381}{6655}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{849}}{605} + \frac{1381}{6655}}}{6} + \frac{17 \sqrt{3}}{363 \sqrt[3]{\frac{3 \sqrt{849}}{605} + \frac{1381}{6655}}}\right) \approx 0.21430884 -0.088940998 i\end{aligned}\]

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

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