Question

If $x+\frac{1}{x}=5$, find the value of $x^2+\frac{1}{x^2}$

Answer 1

$x+\frac{1}{x}=5$

On squaring both sides, we get

${(x+\frac{1}{x})}^2=25$

$\Rightarrow x^2+\frac{1}{x^2}+2\times x\times \frac{1}{x}=25$

$\Rightarrow x^2+\frac{1}{x^2}=25-2$

$\therefore x^2+\frac{1}{x^2}=23$