x^2+x^4=x^6
You asked:
Solve the equation \({x}^{2} + {x}^{4} = {x}^{6}\) for the variable \(x\).
MathBot Answer:
The 5 solutions to the equation are: \[\begin{aligned}x &= 0\\x &= \sqrt{\frac{1}{2} + \frac{\sqrt{5}}{2}} \approx 1.2720196\\x &= \sqrt{- \frac{1}{2} + \frac{\sqrt{5}}{2}} i \approx 0.78615138 i\\x &= - \sqrt{\frac{1}{2} + \frac{\sqrt{5}}{2}} \approx -1.2720196\\x &= - \sqrt{- \frac{1}{2} + \frac{\sqrt{5}}{2}} i \approx -0.78615138 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).