| If \[x-\frac{1}{x}=4,\]then \[\left( x+\frac{1}{x} \right)\]is equal to [SSC (CGL) 2013] |
A) \[5\sqrt{2}\]
B) \[2\sqrt{5}\]
C) (c)\[4\sqrt{2}\]
D) \[4\sqrt{5}\]
Correct Answer: B
Solution :
| \[x-\frac{1}{x}=4\] [given] |
| On squaring both sides, we get |
| \[{{\left( x-\frac{1}{x} \right)}^{2}}={{4}^{2}}\] |
| \[\Rightarrow \]\[{{x}^{2}}+\frac{1}{{{x}^{2}}}-2\times x\times \frac{1}{x}=16\] |
| \[\Rightarrow \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=16+2=18\] |
| On adding 2 both sides, we get |
| \[{{x}^{2}}+\frac{1}{{{x}^{2}}}+2=18+2\] |
| \[\Rightarrow \] \[{{\left( x+\frac{1}{x} \right)}^{2}}=20\] |
| \[\therefore \] \[x+\frac{1}{x}=\sqrt{20}=2\sqrt{5}\] |
You need to login to perform this action.
You will be redirected in
3 sec
