VTMO 2026 - Grade 8 - Final - SET 8 - Self-study Question 2

Numbers $a,b,c,x,y,z$ satisfy $a+b+c=0$, $x+y+z=0$ and $\dfrac{x}{a}+\dfrac{y}{b}+\dfrac{z}{c}=0$. Calculate $A=a^2x+b^2y+c^2z$.