Question

If $3x+\frac{2}{x}=7$ then $(9x^2-\frac{4}{x^2})=?$

Answer 1

$3x+\frac{2}{x}=7\Rightarrow 3x^2-7x+2=0\Rightarrow 3x^2-6x-x+2=0$
$\Rightarrow (3x-1)(x-2)=0$
Put $x=\frac{1}{3}$ and $x=2$ in $9x^2-\frac{4}{x^2}$ which gives $\pm 35$.