A) \[\frac{5}{12}\]
B) \[\frac{12}{5}\]
C) \[\frac{5}{7}\] 0
D) \[\frac{7}{5}\]
Correct Answer: B
Solution :
[b] [Tricky approach] \[\sqrt{\frac{3+x+\sqrt{3-x}}{3+x\sqrt{3-x}}=\frac{2}{1}}\] By componendo and dividendo, \[\Rightarrow \frac{2\sqrt{3+x}}{2\sqrt{3-x}}=\frac{2+1}{2-1}=3\] Squaring both sides, \[\frac{3+x}{3-x}=9\] \[\Rightarrow 3+x=27-\,9x\] \[\Rightarrow 9x+x=27-\,3=24\] \[\Rightarrow x=\frac{24}{10}=\frac{12}{5}\]
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