260000*$X^{3}$ -4*$X^{2}$ +8*$X^{1}$ -4=0

asked by guest
on Nov 25, 2024 at 8:37 am



You asked:

Solve the equation \(260000 {X}^{3} - 4 {X}^{2} + 8 {X}^{1} - 4 = 0\) for the variable \(X\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}X &= \frac{1}{195000} + \sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}} - \frac{389999}{38025000000 \sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}}} \approx 0.024463831\\X &= - \frac{\sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}}}{2} + \frac{1}{195000} + \frac{389999}{76050000000 \sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}}} + i \left(\frac{389999 \sqrt{3}}{76050000000 \sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}}}{2}\right) \approx -0.012224223 + 0.021896124 i\\X &= - \frac{\sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}}}{2} + \frac{1}{195000} + \frac{389999}{76050000000 \sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}}}{2} - \frac{389999 \sqrt{3}}{76050000000 \sqrt[3]{\frac{57036915001}{7414875000000000} + \frac{\sqrt{34222422}}{760500000}}}\right) \approx -0.012224223 -0.021896124 i\end{aligned}\]

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

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