Question

If x=1-underroot2 find x Square +1/x square

Answer 1

Answer:

$x = 1 - \sqrt{2} \\ \\ \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ = > ( {1 - \sqrt{2} })^{2} + \frac{1}{ {(1 - \sqrt{2} })^{2} } \\ \\ \\ = > \frac{(1 - \sqrt{2)^{4} } + 1}{( {1 - \sqrt{2} })^{2} } \\ \\ = > \frac{(1 + 2 - 2 \sqrt{2}) ^{2} + 1 }{1 + 2 - 2 \sqrt{2} } \\ \\ \\ = > \frac{(3 - 2 \sqrt{2} )^{2} + 1 }{3 - 2 \sqrt{2} } \\ \\ = > \frac{9 + 8 - 12 \sqrt{2} + 1 }{3 - 2 \sqrt{2} } \\ \\ = > \frac{18 - 12 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \\ = > \frac{6(3 - 2 \sqrt{2} )}{3 - 2 \sqrt{2} } \\ \\ \\ = > 6$

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