4x^3-9X^2-8x+12=0

what is x

asked by guest
on Nov 16, 2024 at 6:36 am



You asked:

Solve the equation \(4 \cdot {x}^{3} - 9 \cdot {X}^{2} - 8 x + 12 = 0\) for the variable \(x\).

MathBot Answer:

Assuming \(x\) and \(X\) are referring to the same variable.


\(x \in \left\{- \frac{\sqrt[3]{- \frac{243 X^{2}}{8} + \frac{\sqrt{\left(81 - \frac{243 X^{2}}{4}\right)^{2} - 864}}{2} + \frac{81}{2}}}{3} - \frac{2}{\sqrt[3]{- \frac{243 X^{2}}{8} + \frac{\sqrt{\left(81 - \frac{243 X^{2}}{4}\right)^{2} - 864}}{2} + \frac{81}{2}}}, - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{243 X^{2}}{8} + \frac{\sqrt{\left(81 - \frac{243 X^{2}}{4}\right)^{2} - 864}}{2} + \frac{81}{2}}}{3} - \frac{2}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{243 X^{2}}{8} + \frac{\sqrt{\left(81 - \frac{243 X^{2}}{4}\right)^{2} - 864}}{2} + \frac{81}{2}}}, - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{243 X^{2}}{8} + \frac{\sqrt{\left(81 - \frac{243 X^{2}}{4}\right)^{2} - 864}}{2} + \frac{81}{2}}}{3} - \frac{2}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{243 X^{2}}{8} + \frac{\sqrt{\left(81 - \frac{243 X^{2}}{4}\right)^{2} - 864}}{2} + \frac{81}{2}}}\right\}\)

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