| If \[x+(1/x)=2,\] then the value of \[{{x}^{7}}+(1/{{x}^{5}})\] is [SSC (CPO) 2015] |
A) \[{{2}^{5}}\]
B) \[{{2}^{12}}\]
C) 2
D) \[{{2}^{7}}\]
Correct Answer: C
Solution :
| Given, \[x+\frac{1}{x}=2\]\[\Rightarrow \]\[{{x}^{2}}+1=2x\] |
| \[\Rightarrow \] \[{{x}^{2}}-2x+1=0\]\[\Rightarrow \]\[{{(x-1)}^{2}}=0\] |
| \[\Rightarrow \] \[x-1=0\Rightarrow x=1\] |
| \[\therefore \] \[{{x}^{7}}+\frac{1}{{{x}^{5}}}={{(1)}^{7}}+\frac{1}{{{(1)}^{5}}}=1+\frac{1}{1}=1+1=2\] |
You need to login to perform this action.
You will be redirected in
3 sec
