A) \[m-n+1=0\]
B) \[~m+n-1=0\]
C) \[m+n+1=0\]
D) \[m-n-1=0\]
Correct Answer: D
Solution :
(d): \[m=\sqrt{3+\sqrt{3+\sqrt{3+......}}}\] on squaring both sides, \[{{m}^{2}}=3+m\Rightarrow {{m}^{2}}-m=3\] ?..(i) Again, \[n=\sqrt{3-\sqrt{3-\sqrt{3-.....}}}\] On squaring both sides, \[{{n}^{2}}=3-n\] \[\Rightarrow {{n}^{2}}+n=3\] ????(ii) \[\therefore {{m}^{2}}-m={{n}^{2}}+n\Rightarrow \left( {{m}^{2}}-{{n}^{2}} \right)=m+n\] \[\Rightarrow \left( m+n \right)\left( m-n \right)-\left( m+n \right)=0\] \[\Rightarrow \left( m+n \right)\left( m-n-1 \right)=0\]
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