(-60) + 28 / (x^1) + 28/ (x^2) + 28/ (x^3) + 28/ (x^4) = 0

asked by guest
on Jan 07, 2025 at 3:00 am



You asked:

Solve the equation \(-60 + \frac{28}{{x}^{1}} + \frac{28}{{x}^{2}} + \frac{28}{{x}^{3}} + \frac{28}{{x}^{4}} = 0\) for the variable \(x\).

MathBot Answer:

The complex solutions are: \[\left\{\frac{7}{60} + \frac{\sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}{2} + \frac{\sqrt{\left|{- 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}} + \frac{329}{450} + \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{15883}{13500 \sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}}\right|}}{2}, - \frac{\sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}{2} + \frac{7}{60} - \frac{i \sqrt{\left|{- \frac{15883}{13500 \sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}} - 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}} + \frac{329}{450} + \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}\right|}}{2}, - \frac{\sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}{2} + \frac{7}{60} + \frac{i \sqrt{\left|{- \frac{15883}{13500 \sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}} - 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}} + \frac{329}{450} + \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}\right|}}{2}, - \frac{\sqrt{\left|{- 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}} + \frac{329}{450} + \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{15883}{13500 \sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}}\right|}}{2} + \frac{7}{60} + \frac{\sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}{2}\right\} \setminus \left\{0\right\}\]

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

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