Solve y^4-20y^2+64=0

$${ y }^{ 4 } -20 { y }^{ 2 } +64=0$$

Solve for y

$$y=-4$$

$$y=4$$

$$y=2$$

$$y=-2$$

Steps Using the Quadratic Formula

Substitute t for y^{2}.

$$t^{2}-20t+64=0$$

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, -20 for b, and 64 for c in the quadratic formula.

$$t=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 1\times 64}}{2}$$

Do the calculations.

$$t=\frac{20±12}{2}$$

Solve the equation t=\frac{20±12}{2} when ± is plus and when ± is minus.

$$t=16 t=4$$

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

$$y=4 y=-4 y=2 y=-2$$