x^4+2x^2 = 4x^2+6
You asked:
Solve the equation \({x}^{4} + 2 \cdot {x}^{2} = 4 \cdot {x}^{2} + 6\) for the variable \(x\).
MathBot Answer:
The 4 solutions to the equation are: \[\begin{aligned}x &= \sqrt{1 + \sqrt{7}} \approx 1.9093851\\x &= \sqrt{-1 + \sqrt{7}} i \approx 1.2828684 i\\x &= - \sqrt{1 + \sqrt{7}} \approx -1.9093851\\x &= - \sqrt{-1 + \sqrt{7}} i \approx -1.2828684 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).