Question

if x=3+2root2,find the value of xsquare+1/xsquare

Answer 1

Hello Mate

$x = 3 + 2 \sqrt{2} \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \\ \frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \frac{3 - 2 \sqrt{2} }{9 - 8} = 3 - 2 \sqrt{2} \\ { x}^{2} = {(3 + 2 \sqrt{2} )}^{2} \\ = 9 + 8 + 12 \sqrt{2} \\ = 17 + 12 \sqrt{2} \\ \frac{1}{ {x}^{2} } = {(3 - 2 \sqrt{2} )}^{2} \\ = 9 + 8 - 12 \sqrt{2} \\ = 17 - 12 \sqrt{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } \\ 17 + 12 \sqrt{2} + 17 - 12 \sqrt{2} \\ = 34$

Hope it helps☺

Answer 2

hope it helped.............