If the average of s numbers is $r^4$ and the average of r numbers is $s^4$, then find the average of all r + s numbers?

$rs(r^2+s^2-rs)$

Sum of s numbers = s$r^4$

Sum of r numbers = r$s^4$

Sum of r + s = r$s^4$ + s$r^4$

Average of r + s = \(\frac{r\;s^4\;+\;s\;r^4\;}{r + s}\)

                         ⇒ \(\frac{rs (s³ + r³)}{r + s}\)

                         ⇒ \(\frac{rs(s + r)(s² + r² - sr)}{(r + s)}\)

                         ⇒ (s² + r² - sr)