Solve 3x^2-1/x^2+2=0

$$3 { x }^{ 2 } - \frac{ 1 }{ { x }^{ 2 } } +2=0$$

Solve for x (complex solution)

$$x=i$$

$$x=-i$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

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 x^{2}.

$$3x^{2}x^{2}-1+x^{2}\times 2=0$$

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

$$3x^{4}-1+x^{2}\times 2=0$$

Substitute t for x^{2}.

$$3t^{2}+2t-1=0$$

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

$$t=\frac{-2±\sqrt{2^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

Do the calculations.

$$t=\frac{-2±4}{6}$$

Solve the equation t=\frac{-2±4}{6} when ± is plus and when ± is minus.

$$t=\frac{1}{3} t=-1$$

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

$$x=-\frac{\sqrt{3}}{3} x=\frac{\sqrt{3}}{3} x=-i x=i$$

Solve for x

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

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 x^{2}.

$$3x^{2}x^{2}-1+x^{2}\times 2=0$$

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

$$3x^{4}-1+x^{2}\times 2=0$$

Substitute t for x^{2}.

$$3t^{2}+2t-1=0$$

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

$$t=\frac{-2±\sqrt{2^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

Do the calculations.

$$t=\frac{-2±4}{6}$$

Solve the equation t=\frac{-2±4}{6} when ± is plus and when ± is minus.

$$t=\frac{1}{3} t=-1$$

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

$$x=\frac{\sqrt{3}}{3} x=-\frac{\sqrt{3}}{3}$$