Solve x^4+1/x^4-3

$$x ^ { 4 } + \frac { 1 } { x ^ { 4 } } - 3$$

Evaluate

$$x^{4}-3+\frac{1}{x^{4}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4}-3 times \frac{x^{4}}{x^{4}}.

$$\frac{\left(x^{4}-3\right)x^{4}}{x^{4}}+\frac{1}{x^{4}}$$

Since \frac{\left(x^{4}-3\right)x^{4}}{x^{4}} and \frac{1}{x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{4}-3\right)x^{4}+1}{x^{4}}$$

Do the multiplications in \left(x^{4}-3\right)x^{4}+1.

$$\frac{x^{8}-3x^{4}+1}{x^{4}}$$

Factor

$$\frac{\left(x^{4}-\frac{3-\sqrt{5}}{2}\right)\left(x^{4}-\frac{\sqrt{5}+3}{2}\right)}{x^{4}}$$