Question

For what value of $x+\frac{1}{4}\sqrt{x}+a^2$ will be perfect square -

• A. $\pm 1/18$
• B. $\pm 1/8$
• C. $\pm 1/5$
• D. $1/4$

Answer 1

The correct option is B $\pm 1/8$

If $x+\frac{1}{4}\sqrt{x}+a^2$ is a perfect square
then $\frac{1}{4}\sqrt{x}=2\times \sqrt{x}\times (\pm a)$
$\therefore a=\pm \frac{1}{8}$