Question

If x = root 2 -1 then find the value of x2+1/x2

Answer 1

If x = root 2 - 1; then,

$\frac{ {x}^{2} + 1 }{ {x}^{2} } \\ = \frac{( \sqrt{2} - 1)^{2} + 1 }{ {( \sqrt{2} - 1)}^{2} } \\ = \frac{2 - 2 \sqrt{2} + 1 + 1 }{2 - 2 \sqrt{2} + 1} \\ = \frac{4 - 2 \sqrt{2} }{3 - 2 \sqrt{ 2} } \\ = 12 + 8 \sqrt{2} - 3 \sqrt{2} - 8 \\ = 4 + 5 \sqrt{2}$

HOPE THIS COULD HELP!!!