Solve (3)2a=(2/x-x)^2

$$( 3 ) 2 a = ( \frac { 2 } { x } - x ) ^ { 2 }$$

Solve for a

$$a=\frac{\left(x-\frac{2}{x}\right)^{2}}{6}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply 3 and 2 to get 6.

$$6a=\left(\frac{2}{x}-x\right)^{2}$$

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

$$6a=\left(\frac{2}{x}-\frac{xx}{x}\right)^{2}$$

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

$$6a=\left(\frac{2-xx}{x}\right)^{2}$$

Do the multiplications in 2-xx.

$$6a=\left(\frac{2-x^{2}}{x}\right)^{2}$$

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

$$6a=\frac{\left(2-x^{2}\right)^{2}}{x^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-x^{2}\right)^{2}.

$$6a=\frac{4-4x^{2}+\left(x^{2}\right)^{2}}{x^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$6a=\frac{4-4x^{2}+x^{4}}{x^{2}}$$

Multiply both sides of the equation by x^{2}.

$$6ax^{2}=4-4x^{2}+x^{4}$$

The equation is in standard form.

$$6x^{2}a=x^{4}-4x^{2}+4$$

Divide both sides by 6x^{2}.

$$\frac{6x^{2}a}{6x^{2}}=\frac{\left(x^{2}-2\right)^{2}}{6x^{2}}$$

Dividing by 6x^{2} undoes the multiplication by 6x^{2}.

$$a=\frac{\left(x^{2}-2\right)^{2}}{6x^{2}}$$

Solve for x

$$x=\frac{\sqrt{6a+8}+\sqrt{6a}}{2}$$

$$x=\frac{-\sqrt{6a+8}+\sqrt{6a}}{2}$$

$$x=\frac{-\sqrt{6a+8}-\sqrt{6a}}{2}$$

$$x=\frac{\sqrt{6a+8}-\sqrt{6a}}{2}\text{, }a\geq 0$$