x^{3}=x^{9}
You asked:
Solve the equation \({x}^{3} = {x}^{9}\) for the variable \(x\).
MathBot Answer:
The 7 solutions to the equation are: \[\begin{aligned}x &= -1\\x &= 0\\x &= 1\\x &= - \frac{1}{2} - \frac{\sqrt{3} i}{2} \approx -0.5 -0.8660254 i\\x &= - \frac{1}{2} + \frac{\sqrt{3} i}{2} \approx -0.5 + 0.8660254 i\\x &= \frac{1}{2} - \frac{\sqrt{3} i}{2} \approx 0.5 -0.8660254 i\\x &= \frac{1}{2} + \frac{\sqrt{3} i}{2} \approx 0.5 + 0.8660254 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).