VTMO 2026 - Grade 9 - Final - SET 4 - Self-study Question 4

Let $x,y,z$ be real numbers satisfying $x+y+z=5$ and $x^2+y^2+z^2=9$.

a) Prove that $1\le x,y,z\le\dfrac73$.

b) Find the maximum and minimum of $P=xyz$.