Question 32
For $x, y, z \geq 0$, establish the inequality
$$
x(x-z)^2 + y(y-z)^2 \geq (x-z)(y-z)(x+y-z)
$$
and determine when equality holds.
$$
x(x-z)^2 + y(y-z)^2 \geq (x-z)(y-z)(x+y-z)
$$
and determine when equality holds.
MathNet 1992 — Part 01 Question 32
Math Olympiad Vault · MathNet 1992 — Part 01