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)]

$=23$.