Solve IMO in 2 min, International Mathematical Olympiad, 1984, Problem.1

I show a shortcut to solve for International Mathematical Olympiad, IMO, 1984, Problem.1
Prove that 0 ≤ yz + zx + xy − 2xyz ≤ 7/27, where x, y and z are
non-negative real numbers for which x + y + z = 1

[matniet]

Is there a motivation for choosing to expand that particular polynomial after the beginning? Like, how did you come up with that idea?

[KennTollens]

I saw your message on Reddit. You are really good at math. What do you do for work?

[dumbjeeaspirant]

Heyyy
Can you please make a video about Catalan numbers use in calculus????

[giap]

To use the AM-GM inequality, it will require (1-2x), (1-2y) and (1-2z) all be non-negative (which is not true here)

[dumbjeeaspirant]

Here's a question of it

4
∫((x^n/2π)(√((4−x)/x))dx
0