यदि $x=3+2 sqrt{2}$, तो $x^{2}+frac{1}{x^{2}}$ का मूल्य है

$x=3+2 sqrt{2}$

$herefore frac{1}{x}=frac{1}{3+2 sqrt{2}}=frac{1}{3+2 sqrt{2}} imes frac{3-2 sqrt{2}}{3-2 sqrt{2}}$

$=frac{3-2 sqrt{2}}{9-8}=3-2 sqrt{2}$

$x+frac{1}{x}=3+2 sqrt{2}+3-2 sqrt{2}=6$

$herefore x^{2}+frac{1}{x^{2}}=left(x+frac{1}{x} ight)^{2}-2$

= (6)² – 2 = 36 – 2 = 34