xx^3-78x^2+2028x-17576=0

asked by guest
on Oct 22, 2024 at 12:29 pm



You asked:

Solve the equation \(x \cdot {x}^{3} - 78 \cdot {x}^{2} + 2028 x - 17576 = 0\) for the variable \(x\).

MathBot Answer:

The 4 solutions to the equation are: \[\begin{aligned}x &= \frac{\sqrt{104 - 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}} + \frac{4056}{\sqrt{52 + 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}} - \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}} + \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}}{2} - \frac{\sqrt{52 + 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}} - \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}}{2} \approx 8.7323315\\x &= \frac{\sqrt{- \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}} + 52 + 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}{2} - \frac{\sqrt{- \frac{4056}{\sqrt{- \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}} + 52 + 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}} - 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}} + 104 + \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}}{2} \approx 3.8136193 -10.41577 i\\x &= \frac{\sqrt{- \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}} + 52 + 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}{2} + \frac{\sqrt{- \frac{4056}{\sqrt{- \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}} + 52 + 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}} - 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}} + 104 + \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}}{2} \approx 3.8136193 + 10.41577 i\\x &= - \frac{\sqrt{52 + 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}} - \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}}{2} - \frac{\sqrt{104 - 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}} + \frac{4056}{\sqrt{52 + 2 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}} - \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}} + \frac{34138}{3 \sqrt[3]{26364 + \frac{2197 \sqrt{3102567}}{9}}}}}{2} \approx -16.35957\end{aligned}\]

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