Question

If $m-\frac{1}{m}=5$, then find the value of $m^2+\frac{1}{m^2}$.

Answer 1

We have,

$m-\frac{1}{m}=5$

On squaring both sides, we get

$m^2+\frac{1}{m^2}-2=5^2$ ................. Using $(a-b{)}^2=a^2-2ab+b^2$

$m^2+\frac{1}{m^2}=25+2=27$

Hence, this is the answer.