Solve x^2+1/x^2-17/4=0

$$x ^ { 2 } + \frac { 1 } { x ^ { 2 } } - \frac { 17 } { 4 } = 0$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

$$x=\frac{1}{2}=0.5$$

$$x=2$$

$$x=-2$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x^{2}, the least common multiple of x^{2},4.

$$4x^{2}x^{2}+4+4x^{2}\left(-\frac{17}{4}\right)=0$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$4x^{4}+4+4x^{2}\left(-\frac{17}{4}\right)=0$$

Multiply 4 and -\frac{17}{4} to get -17.

$$4x^{4}+4-17x^{2}=0$$

Substitute t for x^{2}.

$$4t^{2}-17t+4=0$$

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 4 for a, -17 for b, and 4 for c in the quadratic formula.

$$t=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 4\times 4}}{2\times 4}$$

Do the calculations.

$$t=\frac{17±15}{8}$$

Solve the equation t=\frac{17±15}{8} when ± is plus and when ± is minus.

$$t=4 t=\frac{1}{4}$$

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

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