| Simplify \[\sqrt{1+{{\left( \frac{{{x}^{4}}-1}{-2{{x}^{2}}} \right)}^{2}}}.\] [SSC (CGL) Pre 2014] |
A) \[\frac{{{x}^{4}}+1}{2{{x}^{2}}}\]
B) \[\frac{\sqrt{{{x}^{2}}+1}}{2{{x}^{2}}}\]
C) \[\frac{{{x}^{4}}+2{{x}^{2}}-1}{2{{x}^{2}}}\]
D) \[\frac{{{x}^{4}}-1}{2{{x}^{2}}}\]
Correct Answer: A
Solution :
| \[\sqrt{1+\left( \frac{{{x}^{4}}-{{1}^{2}}}{-2{{x}^{2}}} \right)}=\sqrt{1+\frac{{{({{x}^{4}}-1)}^{2}}}{4{{x}^{4}}}}\] |
| \[=\sqrt{\frac{4{{x}^{4}}+{{x}^{8}}+1-2{{x}^{4}}}{4{{x}^{4}}}}=\sqrt{\frac{{{({{x}^{4}}+1)}^{2}}}{{{(2{{x}^{2}})}^{2}}}}\] |
| \[=\sqrt{\frac{{{x}^{8}}+2{{x}^{4}}+1}{4{{x}^{4}}}}=\frac{{{x}^{4}}+1}{2{{x}^{2}}}\] |
You need to login to perform this action.
You will be redirected in
3 sec
