Let a, b, c be positive real unequal numbers.

Using the results 1) a^2 + b^2 > 2ab
2) b^2 + c^2 > 2bc
3) c^2 + a^2 > 2ac

Deduce that a^2 - ab + b^2 > ab

Deduce that a^2 + b^2 + c^2 > bc + ac + ab

Show that a^3 + b^3 > ab(a + b)