# If x = $$\Large \sqrt{3} + \sqrt{2}$$, then the value of $$\Large \left(x + \frac{1}{x}\right)$$ is

 A) 2 B) 3 C) $$\Large 2\sqrt{2}$$ D) $$\Large 2\sqrt{3}$$

 D) $$\Large 2\sqrt{3}$$

Given, $$\Large x = \sqrt{3} + \sqrt{2}$$

Therefore, $$\Large \frac{1}{x} = \frac{1}{ \left(\sqrt{3}+\sqrt{2}\right) } \times \frac{ \left(\sqrt{3} - \sqrt{2}\right) }{ \left(\sqrt{3} - \sqrt{2}\right) }$$ [rationalizing]

$$\Large = \frac{1}{x} = \frac{\sqrt{3} - \sqrt{2}}{3 - 2}$$

Therefore, $$\Large x+\frac{1}{x} = \sqrt{3} + \sqrt{2} + \sqrt{3} - \sqrt{2} = 2\sqrt{3}$$

Part of solved questions and answers - Simplification : >> Elementary Mathematics >> Simplification

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