Question

Find the square root of following polynomial $x^4+\frac{1}{x^4}+2$

• A. $|x^2+\frac{1}{x^2}|$
• B. $|x^2-\frac{1}{x^2}|$
• C. $|x+\frac{1}{x}|$
• D. None of these

Answer 1

The correct option is A $|x^2+\frac{1}{x^2}|$

We find the square root of $x^4+\frac{1}{x^4}+2$ as shown below:

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

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

$=\sqrt{{(x^2+\frac{1}{x^2})}^2}(\because (a+b{)}^2=a^2+b^2+2ab)$

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

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

Hence, the square root of $x^4+\frac{1}{x^4}+2$ is $|x^2+\frac{1}{x^2}|$.