2x$^{3}$−7x$^{3}$ +2x−7=0

asked by guest
on Jan 19, 2025 at 8:06 am



You asked:

Solve the equation \(2 {x}^{3} - 7 {x}^{3} + 2 x - 7 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{2}{5 \sqrt[3]{\frac{189}{10} + \frac{3 \sqrt{98745}}{50}}} - \frac{\sqrt[3]{\frac{189}{10} + \frac{3 \sqrt{98745}}{50}}}{3} \approx -1.2374725\\x &= \frac{1}{5 \sqrt[3]{\frac{3 \sqrt{98745}}{50} + \frac{189}{10}}} + \frac{\sqrt[3]{\frac{3 \sqrt{98745}}{50} + \frac{189}{10}}}{6} + i \left(- \frac{\sqrt{3}}{5 \sqrt[3]{\frac{3 \sqrt{98745}}{50} + \frac{189}{10}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{98745}}{50} + \frac{189}{10}}}{6}\right) \approx 0.61873626 + 0.86516108 i\\x &= \frac{1}{5 \sqrt[3]{\frac{3 \sqrt{98745}}{50} + \frac{189}{10}}} + \frac{\sqrt[3]{\frac{3 \sqrt{98745}}{50} + \frac{189}{10}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{98745}}{50} + \frac{189}{10}}}{6} + \frac{\sqrt{3}}{5 \sqrt[3]{\frac{3 \sqrt{98745}}{50} + \frac{189}{10}}}\right) \approx 0.61873626 -0.86516108 i\end{aligned}\]

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

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