A) \[3\sqrt{6}\]
B) \[4\sqrt{6}\]
C) \[5\sqrt{6}\]
D) \[6\sqrt{6}\]
Correct Answer: B
Solution :
\[x=\frac{\sqrt{6}+\sqrt{4}}{\sqrt{6}-\sqrt{4}}=\frac{\left( \sqrt{6}+\sqrt{4} \right)\,\left( \sqrt{6}+\sqrt{4} \right)}{\left( \sqrt{6}-\sqrt{4} \right)\left( \sqrt{6}+\sqrt{4} \right)}\] \[=\,\,\,\,\frac{{{\left( \sqrt{6}+\sqrt{4} \right)}^{2}}}{2}=\frac{6+4+2\sqrt{24}}{2}\] \[=\frac{10+4\sqrt{6}}{2}=5+2\sqrt{6}\] \[=\,\,\,\,\,\,\,y=\frac{\sqrt{6}-\sqrt{4}}{\sqrt{6}+\sqrt{4}}\,\,\,\,\,\,\,\therefore \,\,\,\,\,\,y=\frac{1}{x}\] \[=\,\,\,\,\,\,\,\frac{1}{5+2\sqrt{6}}\times \frac{5-2\sqrt{6}}{5-2\sqrt{6}}\] \[=\,\,\,\,\,\,\,\frac{5-2\sqrt{6}}{25-24}=5-2\sqrt{6}\] \[\therefore \,\,\,\,\,\,\,x-y=5+2\sqrt{6}-5+2\sqrt{6}=\underline{\mathbf{4}\sqrt{\mathbf{6}}}\]
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