Question

Simplify $\sqrt{1+{\left(\frac{x^4}{-2x^2}\right)}^2}$

• A. $\frac{x^4+1}{2x^2}$
• B. $\frac{\sqrt{x^2+1}}{2}$
• C. $\frac{x^4+2x^2-1}{2x^2}$
• D. $\frac{x^4-1}{2x^4}$

Answer 1

Answer: (B)

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

$\sqrt{1+(\frac{x^4}{-2x^2}{)}^2}$

$\Rightarrow \sqrt{1+\frac{x^8}{4x^4}}$

$\Rightarrow \sqrt{\frac{4x^4+x^8}{4x^4}}$

$\Rightarrow \frac{\sqrt{4x^4+x^8}}{2x^2}$

$\Rightarrow \frac{\sqrt{x^2+1}}{2}$