A) \[2\sqrt{5}\]
B) \[2\sqrt{6}\]
C) \[1+\sqrt{6}\]
D) \[1+\sqrt{5}\]
Correct Answer: A
Solution :
| \[\sqrt{11+2\sqrt{30}}-\frac{1}{\sqrt{11+2\sqrt{30}}}\] |
| \[=\sqrt{6+5+2\sqrt{5}\sqrt{6}}-\frac{1}{\sqrt{11+2\sqrt{30}}}\] |
| \[=\sqrt{{{(\sqrt{6})}^{2}}+{{(\sqrt{5})}^{2}}+2\sqrt{5}\sqrt{6}}-\sqrt{{{(\sqrt{6})}^{2}}+{{(\sqrt{5})}^{2}}+2\sqrt{5}\sqrt{6}}\] |
| \[=\sqrt{{{(\sqrt{6}+\sqrt{5})}^{2}}}-\frac{1}{\sqrt{{{(\sqrt{6}+\sqrt{5})}^{2}}}}\] |
| \[=\sqrt{6+}\sqrt{5}-\frac{1}{\sqrt{6}+\sqrt{5}}\times \frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}-\sqrt{5}}\] |
| \[=\sqrt{6}+\sqrt{5}-\frac{(\sqrt{6}-\sqrt{5})}{6-5}\] |
| \[=\sqrt{6}+\sqrt{5}-(\sqrt{6}-\sqrt{5})\] |
| \[=\sqrt{6}+\sqrt{5}-\sqrt{6}+\sqrt{5}\] |
| \[=2\sqrt{5}\] |
You need to login to perform this action.
You will be redirected in
3 sec
