Question 2Let $a,b,c$ be real numbers such that $0<a,b,c<1/2$ and $a+b+c=1$. Prove that for all real numbers $x,y,z$, $$abc(x+y+z)^2\ge ayz(1-2a)+bxz(1-2b)+cxy(1-2c).$$ When does equality hold?