Question

if x = 2 + squareroot of 3, 1/x=?​

Answer 1

Answer:

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

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