Question

if x=2-root3 find the value of x+(1/x)​

Answer 1

$x = 2 - \sqrt{3}$

$\frac{1}{x} = \frac{1}{2 - \sqrt{3} } \\ = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{2 + \sqrt{3} }{ {2}^{2} - \sqrt{3}^{2} } = \frac{2 + \sqrt{3} }{4 - 3} \\ = 2 + \sqrt{3}$

We need to find,

$x + \frac{1}{x} = 2 - \sqrt{3} + 2 + \sqrt{3} \\ x + \frac{1}{x} = 4$

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