| If \[x=\sqrt{8+\sqrt{8+\sqrt{8...}}}\]and \[y=\sqrt{8-\sqrt{8-\sqrt{8....,}}}\] |
A) \[x+y=1\]
B) \[x+y+1=0\]
C) \[x-y=1\]
D) \[x-y+1=0\]
Correct Answer: C
Solution :
| \[x=\sqrt{8+\sqrt{8+\sqrt{8+...}}}\] |
| \[{{x}^{2}}=8+\sqrt{8\sqrt{8+\sqrt{8+...}}}\] |
| \[\therefore \] \[{{x}^{2}}=8+x\] |
| Similarly, \[{{y}^{2}}=8-y\] |
| \[\therefore \] \[{{x}^{2}}-{{y}^{2}}=(x+8)-(8-y)\] |
| \[(x+y)(x-y)=(x+y)\] |
| \[\Rightarrow \] \[x-y=1\] |
You need to login to perform this action.
You will be redirected in
3 sec
