x^4 = 4*x

asked by guest
on Sep 20, 2024 at 2:42 am



You asked:

Solve the equation \({x}^{4} = 4 x\) for the variable \(x\).

MathBot Answer:

The 4 solutions to the equation are: \[\begin{aligned}x &= 0\\x &= 2^{\frac{2}{3}} \approx 1.5874011\\x &= - \frac{2^{\frac{2}{3}}}{2} - \frac{2^{\frac{2}{3}} \sqrt{3} i}{2} \approx -0.79370053 -1.3747296 i\\x &= - \frac{2^{\frac{2}{3}}}{2} + \frac{2^{\frac{2}{3}} \sqrt{3} i}{2} \approx -0.79370053 + 1.3747296 i\end{aligned}\]

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

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