A) 0
B) 1
C) 2
D) 3
Correct Answer: A
Solution :
\[\frac{1}{\sqrt{12-\sqrt{140}}}-\frac{1}{\sqrt{8-\sqrt{60}}}-\frac{2}{\sqrt{10+\sqrt{84}}}\] \[=\frac{1}{\sqrt{{{(7)}^{2}}+{{(\sqrt{5})}^{2}}-2\sqrt{7}\cdot \sqrt{5}}}-\frac{1}{\sqrt{{{(\sqrt{5})}^{2}}+{{(\sqrt{3})}^{2}}-2\sqrt{5}\cdot \sqrt{3}}}\] \[-\frac{2}{\sqrt{{{(\sqrt{7})}^{2}}+{{(\sqrt{3})}^{2}}-2\sqrt{7}\cdot \sqrt{3}}}\] \[=\frac{1}{\sqrt{(\sqrt{7}}-{{\sqrt{5}}^{2}})}-\frac{1}{\sqrt{{{(\sqrt{5}-\sqrt{3})}^{2}}}}-\frac{2}{{{(\sqrt{7}+\sqrt{3})}^{2}}}\] \[=\frac{1}{\sqrt{7}-\sqrt{5}}-\frac{1}{\sqrt{5}-\sqrt{3}}-\frac{2}{\sqrt{7}+\sqrt{3}}\] \[=\frac{\sqrt{7}+\sqrt{5}}{2}-\frac{\sqrt{5}+\sqrt{3}}{2}-\frac{\sqrt{7}-\sqrt{3}}{2}\] \[=\frac{1}{2}(\sqrt{7}+\sqrt{5}-\sqrt{5}-\sqrt{3}-\sqrt{7}+\sqrt{3})\] = 0
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