VTMO 2026 - Grade 9 - Semifinal - SET 2 - Self-study Question 13

Real numbers x,y,z satisfy $x+y+z=0$ and $\dfrac{x(x+2y)}{y(y+2z)}=\dfrac1{2024}$. Find $P=\dfrac{z^2+2xz}{x^2+2xy}$.