Solve (1/x+1/x)^2=1

$$( \frac { 1 } { x } + \frac { 1 } { x } ) ^ { 2 } = 1$$

Solve for x

$$x=-2$$

$$x=2$$

Steps by Finding Square Root

Combine \frac{1}{x} and \frac{1}{x} to get 2\times \frac{1}{x}.

$$\left(2\times \frac{1}{x}\right)^{2}=1$$

Express 2\times \frac{1}{x} as a single fraction.

$$\left(\frac{2}{x}\right)^{2}=1$$

To raise \frac{2}{x} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4}{x^{2}}=1$$

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

$$4=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Combine \frac{1}{x} and \frac{1}{x} to get 2\times \frac{1}{x}.

$$\left(2\times \frac{1}{x}\right)^{2}=1$$

Express 2\times \frac{1}{x} as a single fraction.

$$\left(\frac{2}{x}\right)^{2}=1$$

To raise \frac{2}{x} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4}{x^{2}}=1$$

Subtract 1 from both sides.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

Since \frac{4}{x^{2}} and \frac{x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 4}}{2\left(-1\right)}$$

Multiply 4 times 4.

$$x=\frac{0±\sqrt{16}}{2\left(-1\right)}$$

Take the square root of 16.

$$x=\frac{0±4}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±4}{-2}$$

Now solve the equation x=\frac{0±4}{-2} when ± is plus. Divide 4 by -2.

$$x=-2$$

Now solve the equation x=\frac{0±4}{-2} when ± is minus. Divide -4 by -2.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$