Question

If $3x+\frac{2}{x}=7$. Find the value of $(9x^2+\frac{4}{x^2})$.

Answer 1

We have,

$3x+\frac{2}{x}=7$

On squaring both sides, we get

${(3x+\frac{2}{x})}^2=7^2$

$(9x^2+\frac{4}{x^2}+2\times 3x\times \frac{2}{x})=49$

$(9x^2+\frac{4}{x^2}+12)=49$

$(9x^2+\frac{4}{x^2})=49-12$

$(9x^2+\frac{4}{x^2})=37$

Hence, this is the answer.