Question

If $a^2+\frac{9}{a^2}=31$, what is the value of $a-\frac{3}{a}$?

Answer 1

Given: $a^2+\frac{9}{a^2}=31$

To find $\to a-\frac{3}{a}$

${(a-\frac{3}{a})}^2=a^2+\frac{9}{a^2}-2\left(a\right)\left(\frac{3}{a}\right)$

${(a-\frac{3}{a})}^2=31-6$

${(a-\frac{3}{a})}^2=25$

$a-\frac{3}{a}=\pm 5$.