Question

If x is equal to 2 - √3 then what is the value of x + 1 / x?

Answer 1

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Here is your answer
$x + \frac{1}{x} \\ = 2 - \sqrt{3} + \frac{1}{2 - \sqrt{3} } \\ = 2 - \sqrt{3} + \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ = 2 - \sqrt{3} + \frac{2 + \sqrt{3} }{2 {}^{2} - (\sqrt{3} ) {}^{2} } \\ = 2 - \sqrt{3} + \frac{2 + \sqrt{3} }{4 - 3} \\ = 2 - \sqrt{3} + 2 + \sqrt{3} \\ = 4$

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