SMO 2009 Senior Round 2 Question 4

Let $a,b,c\gt 0$ such that $a+b+c=1$. Show that if $x_1,x_2,\ldots,x_5$ are positive real numbers such that $x_1x_2\cdots x_5=1$, then $$(ax_1^2+bx_1+c)(ax_2^2+bx_2+c)\cdots(ax_5^2+bx_5+c)\ge1.$$