Solve x^4-9x^2+8=0?

$$x ^ { 4 } - 9 x ^ { 2 } + 8 = 0 ?$$

Solve for x

$$x=-2\sqrt{2}\approx -2.828427125$$

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-9t+8=0$$

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, -9 for b, and 8 for c in the quadratic formula.

$$t=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 1\times 8}}{2}$$

Do the calculations.

$$t=\frac{9±7}{2}$$

Solve the equation t=\frac{9±7}{2} when ± is plus and when ± is minus.

$$t=8 t=1$$

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

$$x=2\sqrt{2} x=-2\sqrt{2} x=1 x=-1$$