Question

If $x+\frac{1}{x}=3$ then $x^2+\frac{1}{x^2}$

Answer 1

${(x+\frac{1}{x})}^2=x^2+\frac{1}{x^2}+2\times x\times \frac{1}{x}$

$\Rightarrow {\left(3\right)}^2=x^2+\frac{1}{x^2}+2$

$\Rightarrow 9=x^2+\frac{1}{x^2}+2$

$\Rightarrow x^2+\frac{1}{x^2}+2=9$

$\Rightarrow x^2+\frac{1}{x^2}=9-2=7$

$\therefore x^2+\frac{1}{x^2}=7$