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Question 101
If $$\frac{1}{N}=\frac{(\sqrt{6}+\sqrt{5})}{\sqrt{6}-\sqrt{5}}$$, then what is the value of N ?
Solution
Given : $$\frac{1}{N}=\frac{\sqrt6+\sqrt5}{\sqrt6-\sqrt5}$$
=> $$N=\frac{\sqrt6-\sqrt5}{\sqrt6+\sqrt5}$$
Rationalizing the denominator, we get :
=> $$N=\frac{\sqrt6-\sqrt5}{\sqrt6+\sqrt5}\times\frac{\sqrt6-\sqrt5}{\sqrt6-\sqrt5}$$
=> $$N=\frac{(\sqrt6-\sqrt5)^2}{(\sqrt6+\sqrt5)(\sqrt6-\sqrt5)}$$
=> $$N=\frac{6+5-2(\sqrt6)(\sqrt5)}{6-5}$$
=> $$N=11-2\sqrt{30}$$
=> Ans - (C)
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