Solve m^4+1/m^4=2

$$m ^ { 4 } + \frac { 1 } { m ^ { 4 } } = 2$$

Solve for m

$$m=1$$

$$m=-1$$

Steps Using the Quadratic Formula

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by m^{4}.

$$m^{4}m^{4}+1=2m^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$m^{8}+1=2m^{4}$$

Subtract 2m^{4} from both sides.

$$m^{8}+1-2m^{4}=0$$

Substitute t for m^{4}.

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

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, -2 for b, and 1 for c in the quadratic formula.

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

Do the calculations.

$$t=\frac{2±0}{2}$$

Solutions are the same.

$$t=1$$

Since m=t^{4}, the solutions are obtained by evaluating m=±\sqrt[4]{t} for positive t.

$$m=-1 m=1$$