Question

. If x = 2 + √ 3, then find the value of x +1/x

.

Answer 1

here is your answer... hope it helps

Answer 2

Hey mate!

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Given :

$x = 2 + \sqrt{3}$

To find :

$x + \frac{1}{x}$

Solution :

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

Now,

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

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Thanks for the question !

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