x to the power of 6 - 7xcubed - 8=0
You asked:
Solve the equation \({x}^{6} - 7 {x}^{3} - 8 = 0\) for the variable \(x\).
MathBot Answer:
The 6 solutions to the equation are: \[\begin{aligned}x &= -1\\x &= 2\\x &= -1 + \sqrt{3} i = -1 + 1.7320508 i\\x &= -1 - \sqrt{3} i = -1 -1.7320508 i\\x &= \frac{1}{2} - \frac{\sqrt{3} i}{2} \approx 0.5 -0.8660254 i\\x &= \frac{1}{2} + \frac{\sqrt{3} i}{2} \approx 0.5 + 0.8660254 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).