((x^4)/4)+1=3+x

asked by guest
on Sep 19, 2024 at 3:41 pm



You asked:

Solve the equation \(\frac{{x}^{4}}{4} + 1 = 3 + x\) for the variable \(x\).

MathBot Answer:

The 4 solutions to the equation are: \[\begin{aligned}x &= 2\\x &= - \frac{2}{3} - \frac{\sqrt[3]{26 + 6 \sqrt{33}}}{3} + \frac{8}{3 \sqrt[3]{26 + 6 \sqrt{33}}} \approx -1.2955977\\x &= - \frac{2}{3} - \frac{4}{3 \sqrt[3]{26 + 6 \sqrt{33}}} + \frac{\sqrt[3]{26 + 6 \sqrt{33}}}{6} + i \left(\frac{4 \sqrt{3}}{3 \sqrt[3]{26 + 6 \sqrt{33}}} + \frac{\sqrt{3} \sqrt[3]{26 + 6 \sqrt{33}}}{6}\right) \approx -0.35220113 + 1.7214332 i\\x &= - \frac{2}{3} - \frac{4}{3 \sqrt[3]{26 + 6 \sqrt{33}}} + \frac{\sqrt[3]{26 + 6 \sqrt{33}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{26 + 6 \sqrt{33}}}{6} - \frac{4 \sqrt{3}}{3 \sqrt[3]{26 + 6 \sqrt{33}}}\right) \approx -0.35220113 -1.7214332 i\end{aligned}\]

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

+ Submit Question