Solve x^4-6x^2+4=0

$${ x }^{ 4 } -6 { x }^{ 2 } +4=0$$

Solve for x

$$x=\frac{\sqrt{2}-\sqrt{10}}{2}\approx -0.874032049$$

$$x=\frac{\sqrt{10}-\sqrt{2}}{2}\approx 0.874032049$$

$$x = \frac{\sqrt{2} + \sqrt{10}}{2} \approx 2.288245611$$

$$x=\frac{-\sqrt{2}-\sqrt{10}}{2}\approx -2.288245611$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-6t+4=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -6 for b, and 4 for c in the quadratic formula.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\times 4}}{2}$$

Do the calculations.

$$t=\frac{6±2\sqrt{5}}{2}$$

Solve the equation t=\frac{6±2\sqrt{5}}{2} when ± is plus and when ± is minus.

$$t=\sqrt{5}+3 t=3-\sqrt{5}$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.

$$x=\frac{\sqrt{2}+\sqrt{10}}{2} x=-\frac{\sqrt{2}+\sqrt{10}}{2} x=-\frac{\sqrt{2}-\sqrt{10}}{2} x=\frac{\sqrt{2}-\sqrt{10}}{2}$$