Question
Find the arithmetic mean of:
$(m + n)^2$ and $(m - n)^2$
$(m + n)^2$ and $(m - n)^2$
✓
Answer
Arithmetic mean of $(m+n)^2$ and $(m-n)^2=\frac{(m+n)^2+(m-n)^2}{2}$
$=\frac{m^2+n^2+2 m n+m^2+n^2-2 m n}{2}$
$=\frac{2\left(m^2+n^2\right)}{2}$
$ =m^2+n^2$
$=\frac{m^2+n^2+2 m n+m^2+n^2-2 m n}{2}$
$=\frac{2\left(m^2+n^2\right)}{2}$
$ =m^2+n^2$
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