Too much

Author: daniyar
Problem has been solved: 25 times

Русский язык | English Language

Let $a$ and $b$ be such (not necessarily real) numbers such that the equalities $\frac {a ^ 2 + b ^ 2} {a + b} = 4$ and $\frac {a ^ 4 + b ^ 4} {a ^ 3 + b ^ 3} = 2$. Find the sum of all possible values of the fraction $\frac {a ^ 6 + b ^ 6} {a ^ 5 + b ^ 5}$