Question

if x = 3 +2under root 2 find x +1/x​

Answer 1

Answer:

6

Step-by-step explanation:

First we have to find the value of

$\frac{1}{x} \\ \frac{1}{x } = \frac{1}{3 + \sqrt{2} } \times \frac{3 - \sqrt{2} }{3 - \sqrt{2} } \\ = \frac{3 - \sqrt{2} }{ {3}^{2} - { \sqrt{2} }^{2} } = \frac{3 - \sqrt{2} }{3 - 2} \\ x = 3 - \sqrt{2} \\ now \: we \: can \: find \: it \: \\ x + \frac{1}{x} = 3 + \sqrt{2} + 3 - \sqrt{2} \\ = 3 + 3 = 6 \\ so \: x + \frac{1}{x} = 6$

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