Question 69
For positive real numbers $a$, $b$, $c$, which of the following statements necessarily implies $a = b = c$:
(I) $a(b^3 + c^3) = b(c^3 + a^3) = c(a^3 + b^3)$,
(II) $a(a^3 + b^3) = b(b^3 + c^3) = c(c^3 + a^3)$?
Justify your answer.
(I) $a(b^3 + c^3) = b(c^3 + a^3) = c(a^3 + b^3)$,
(II) $a(a^3 + b^3) = b(b^3 + c^3) = c(c^3 + a^3)$?
Justify your answer.