Question

If
$x = 3 + 2 \sqrt{2}$
then find
${x}^{2} + \frac{1}{ {x}^{2} }$
Please help

Answer 1

if x=3+2√2
then
$\frac{1}{x} = \frac{1}{3 + 2 \sqrt{2 } } = 3 - 2 \sqrt{2}$
then x²+1/x²=(3+2√2)²+(3-2√2)²
=2{3²+(2√2)²}
=2(9+8)
=2*17
=34..............(ans)