Quantitative Aptitude Ques 257

Question: Simplify $ \sqrt{1+{{( \frac{x^{4}-1}{-2x^{2}} )}^{2}}}. $

Options:

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

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

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

D) $ \frac{x^{4}-1}{2x^{2}} $

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \sqrt{1+( \frac{x^{4}-1^{2}}{-2x^{2}} )}=\sqrt{1+\frac{{{(x^{4}-1)}^{2}}}{4x^{4}}} $ $ =\sqrt{\frac{4x^{4}+x^{8}+1-2x^{4}}{4x^{4}}}=\sqrt{\frac{{{(x^{4}+1)}^{2}}}{{{(2x^{2})}^{2}}}} $ $ =\sqrt{\frac{x^{8}+2x^{4}+1}{4x^{4}}}=\frac{x^{4}+1}{2x^{2}} $
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