Solve left(x^2right)^2-3x^2+1=0

$${ \left( { x }^{ 2 } \right) }^{ 2 } -3 { x }^{ 2 } +1=0$$

Solve for x

$$x=\frac{1-\sqrt{5}}{2}\approx -0.618033989$$

$$x=\frac{\sqrt{5}-1}{2}\approx 0.618033989$$

$$x = \frac{\sqrt{5} + 1}{2} \approx 1.618033989$$

$$x=\frac{-\sqrt{5}-1}{2}\approx -1.618033989$$

Steps Using the Quadratic Formula

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-3x^{2}+1=0$$

Substitute t for x^{2}.

$$t^{2}-3t+1=0$$

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, -3 for b, and 1 for c in the quadratic formula.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 1\times 1}}{2}$$

Do the calculations.

$$t=\frac{3±\sqrt{5}}{2}$$

Solve the equation t=\frac{3±\sqrt{5}}{2} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{5}+3}{2} t=\frac{3-\sqrt{5}}{2}$$

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

$$x=\frac{\sqrt{5}+1}{2} x=-\frac{\sqrt{5}+1}{2} x=-\frac{1-\sqrt{5}}{2} x=\frac{1-\sqrt{5}}{2}$$