2x^3-3x+2=0

asked by guest
on Oct 06, 2024 at 11:19 am



You asked:

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

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{3}{2 \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{2}}{4}}} - \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{2}}{4}}}{3} \approx -1.4756865\\x &= \frac{3}{4 \sqrt[3]{\frac{27 \sqrt{2}}{4} + \frac{27}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2}}{4} + \frac{27}{2}}}{6} + i \left(- \frac{3 \sqrt{3}}{4 \sqrt[3]{\frac{27 \sqrt{2}}{4} + \frac{27}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2}}{4} + \frac{27}{2}}}{6}\right) \approx 0.73784326 + 0.36501784 i\\x &= \frac{3}{4 \sqrt[3]{\frac{27 \sqrt{2}}{4} + \frac{27}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2}}{4} + \frac{27}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2}}{4} + \frac{27}{2}}}{6} + \frac{3 \sqrt{3}}{4 \sqrt[3]{\frac{27 \sqrt{2}}{4} + \frac{27}{2}}}\right) \approx 0.73784326 -0.36501784 i\end{aligned}\]

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

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