Question 101

If N = (√6 - √5)/(√6 + √5), then what is the value of N + (1/N)?

Solution

Given N = (√6 - √5)/(√6 + √5)

Now, N + (1/N) = $$\frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}}$$ + $$\frac{\sqrt{6} + \sqrt{5}}{\sqrt{6} - \sqrt{5}}$$

$$\Rightarrow 6 + 5 - 2\sqrt{30} + 6 + 5 + 2\sqrt{30}$$ = 11 + 11 = 22

Hence, option D is the correct answer.

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