| If \[x=\sqrt{12+\sqrt{12+\sqrt{12+\sqrt{12+...}}}}\]and \[y=\sqrt{12-\sqrt{12-\sqrt{12-\sqrt{12-...}}}},\]then the value of \[x-y\]will be |
A) 0
B) 1
C) 4
D) 2
Correct Answer: B
Solution :
| \[x=\sqrt{12+\sqrt{12+\sqrt{12+}}}...=\sqrt{12+x}\] |
| \[\Rightarrow \]\[\sqrt{12+x}=x\]is satisfied for \[x=4\] |
| \[y=\sqrt{12-\sqrt{12-\sqrt{12}-}}...=\sqrt{12-y}\] |
| \[\Rightarrow \]\[\sqrt{12-y}=y\]is satisfied for \[y=3\] |
| \[\therefore \]\[x-y=4-3=1\] |
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