Question 43
Let $a, b, c, d, e$ be real numbers such that $a+b+c+d+e=0$. Let, also $A=ab+bc+cd+de+ea$ and $B=ac+ce+eb+bd+da$.
Show that
$$
2005 A+B \leq 0 \text{or} \quad A+2005 B \leq 0
$$
Show that
$$
2005 A+B \leq 0 \text{or} \quad A+2005 B \leq 0
$$