A) \[\frac{17}{21}\]
B) 1
C) \[\frac{263}{20}\]
D) \[\frac{331}{5}\]
Correct Answer: C
Solution :
| [c] \[\frac{\sqrt{x+4}+\sqrt{x-10}}{\sqrt{x+4}-\sqrt{x-10}}=\frac{5}{2}\] On applying componendo and dividendo rule, we get \[\frac{\sqrt{x+4}+\sqrt{x-10}+\sqrt{x+4}-\sqrt{x-10}}{\sqrt{x+4}+\sqrt{x-10}-\sqrt{x+4}+\sqrt{x-10}}\] \[=\frac{5+2}{5-2}\]\[\Rightarrow \]\[\frac{2\sqrt{x+4}}{2\sqrt{x-10}}=\frac{7}{3}\] \[\Rightarrow \]\[\frac{\sqrt{x+4}}{x-10}=\frac{7}{3}\] Squaring on both sides, we get \[\Rightarrow \] \[\frac{x+4}{x-10}=\frac{49}{9}\] \[\Rightarrow \] \[9x+36=49x-490\] \[\Rightarrow \] \[49x-9x=490+36\] \[\Rightarrow \] \[40x=526\] \[\therefore \] \[x=\frac{526}{40}=\frac{263}{20}\] |
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