VTMO 2026 - Grade 9 - Semifinal - SET 2 - Self-study Question 16

Real numbers x,y,z satisfy $x+y+z=5$ and $x^2+y^2+z^2=9$. (a) Prove $1\le x,y,z\le7/3$. (b) Find the greatest and smallest values of $P=xyz$.