Question 1

# If $$N=(\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}})$$, then what is the value of $$\frac{1}{N}$$ ?

Solution

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)