If $$N=(\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}})$$, then what is the value of $$\frac{1}{N}$$ ?
Given : $$N=\frac{\sqrt7-\sqrt5}{\sqrt7+\sqrt5}$$
=> $$\frac{1}{N}=\frac{\sqrt7+\sqrt5}{\sqrt7-\sqrt5}$$
Rationalizing the denominator, we get :
= $$\frac{\sqrt7+\sqrt5}{\sqrt7-\sqrt5}\times\frac{\sqrt7+\sqrt5}{\sqrt7+\sqrt5}$$
= $$\frac{(\sqrt7+\sqrt5)^2}{(\sqrt7-\sqrt5)(\sqrt7+\sqrt5)}$$
= $$\frac{7+5+2(\sqrt7)(\sqrt5)}{7-5}$$
= $$\frac{12+2\sqrt{35}}{2}=6+\sqrt{35}$$
=> Ans - (B)
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