Question

x=9+4 root5 find the value of x^2+1/x^2

Answer 1

Gn that,

$x = 9 + 4 \sqrt{5}$
therefore
${x}^{2} = {(9 + 4 \sqrt{5} })^{2}$
ie

${ x}^{2} = 81 + 72 \sqrt{5} + 5$
ie

${x}^{2} = 86 + 72 \sqrt{5}$
Next,
$\frac{ {x}^{2} + 1 }{ {x}^{2} } = \frac{86 + 72 \sqrt{5} + 1}{86 + 72 \sqrt{5} } = \frac{87 + 72 \sqrt{5} }{86 + 72 \sqrt[1]{5} }$
ie

Answer 2

solution is attached here in file