| \[\sqrt{56+\sqrt{56+\sqrt{56}}}+...\div {{2}^{2}}=?\] |
A) 0
B) 1
C) 2
D) 8
E) None of these
Correct Answer: C
Solution :
| Let \[\sqrt{56+\sqrt{56+\sqrt{56}}}+...=x\] |
| \[\sqrt{56+x}=x\] |
| On squaring both side, we get \[{{(\sqrt{56+x})}^{2}}={{x}^{2}}\] |
| \[\Rightarrow \] \[56+x={{x}^{2}}\] |
| \[\Rightarrow \] \[{{x}^{2}}-x-56=0\] |
| \[\Rightarrow \]\[{{x}^{2}}-8x+7x-56=0\] |
| \[\Rightarrow \]\[x\,(x-8)+7\,\,(x-8)=0\]\[\Rightarrow \]\[x=8\] |
| \[\therefore \] \[\sqrt{56+\sqrt{56+\sqrt{56}}}=8\] |
| So, \[\frac{8}{{{(2)}^{2}}}=\frac{8}{4}=2\] |
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