$x^{3}$ -6 $x^{2}$ -11x-6=0

asked by guest
on Oct 24, 2024 at 2:24 pm



You asked:

Solve the equation \({x}^{3} - 6 \cdot {x}^{2} - 11 x - 6 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= 2 + \sqrt[3]{22 + \frac{\sqrt{2703}}{9}} + \frac{23}{3 \sqrt[3]{22 + \frac{\sqrt{2703}}{9}}} \approx 7.5600055\\x &= - \frac{\sqrt[3]{\frac{\sqrt{2703}}{9} + 22}}{2} - \frac{23}{6 \sqrt[3]{\frac{\sqrt{2703}}{9} + 22}} + 2 + i \left(- \frac{23 \sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{2703}}{9} + 22}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2703}}{9} + 22}}{2}\right) \approx -0.78000275 + 0.43040205 i\\x &= - \frac{\sqrt[3]{\frac{\sqrt{2703}}{9} + 22}}{2} - \frac{23}{6 \sqrt[3]{\frac{\sqrt{2703}}{9} + 22}} + 2 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2703}}{9} + 22}}{2} + \frac{23 \sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{2703}}{9} + 22}}\right) \approx -0.78000275 -0.43040205 i\end{aligned}\]

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

+ Submit Question