Question

Express $4x^2+2+\frac{1}{4x^2}$ as a perfect square.

Answer 1

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

$={\left(2x\right)}^2+2\times 2x\times \frac{1}{2x}+\frac{1}{{\left(2x\right)}^2}$ is of the form $a^2+2ab+b^2={(a+b)}^2$

$={(2x+\frac{1}{2x})}^2$ is a perfect square.