Question

If $m-\frac{1}{m}=5$, find: $m^2+\frac{1}{m^2}$.

Answer 1

Given,

$m-\frac{1}{m}=5$......(1).

Then,

$m^2+\frac{1}{m^2}$

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

$=5^2+2$ [ Using (1)]

$=27$.