Question 169
Let $x$, $y$, $z$ be positive real numbers such that $x + y + z = 1$. For positive integer $n$, define $S_n = x^n + y^n + z^n$. Furthermore, let $P = S_2 S_{2005}$ and $Q = S_3 S_{2004}$.
a. Find the smallest possible value of $Q$.
b. If $x$, $y$, $z$ are pairwise distinct, determine whether $P$ or $Q$ is larger.
a. Find the smallest possible value of $Q$.
b. If $x$, $y$, $z$ are pairwise distinct, determine whether $P$ or $Q$ is larger.