VTMO 2026 - Grade 8 - Semifinal - SET 06 - Self-study Question 3

For real numbers $x,y,z,t\in[1/3,1]$, find the greatest and least values of $P=\dfrac{y+z+t}{1+x}+\dfrac{x+z+t}{1+y}+\dfrac{x+y+t}{1+z}+\dfrac{x+y+z}{1+t}$.