Question

If x= 1 - √2, find the value of
(1). x +1/x
(2). x2 + 1/x2
​

Answer 1

Step-by-step explanation:

$x = 1 - \sqrt{2} \\ \\ 1)x + \frac{1}{x} \\ \\ 1 - \sqrt{2} + \frac{1}{1 - \sqrt{2} } \\ \\ \frac{ {(1 - \sqrt{2} ) }^{2} + 1 }{1 - \sqrt{2} } \\ \\ \frac{1 + 2 - 2 \sqrt{2} + 1}{1 - \sqrt{2} } \\ \\ \frac{4 - 2 \sqrt{2} }{1 - \sqrt{2} } \\ \\ \frac{-2\sqrt2(1 - \sqrt{2}) }{1 - \sqrt{2} } \\ \\ - 2 \sqrt2 \\ \\ \\ \\ 2) {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ {(1 - \sqrt{2} )}^{2} + \frac{1}{ {(1 - \sqrt{2}) }^{2} } \\ \\ 1 + 2 - 2 \sqrt{2} + \frac{1}{1 + 2 - 2 \sqrt{2} } \\ \\ 3 - 2 \sqrt{2} + \frac{1}{3 - 2 \sqrt{2} } \\ \\ \frac{ {(3 - 2 \sqrt{2}) }^{2} + 1}{3 - 2 \sqrt{2} } \\ \\ \frac{9 + 8 - 12 \sqrt{2} + 1 }{3 - 2 \sqrt{2} } \\ \\ \frac{18 - 12 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \\ \frac{6(3- 2 \sqrt{2}) }{3 - 2 \sqrt{2} }$

= 6