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evagelos
Jun13-10, 08:14 PM
1. The problem statement, all variables and given/known data

Prove: xyzw\geq x+y+z+w-3,where x\geq 1,y\geq 1,z\geq 1,w\geq 1

2. Relevant equations



3. The attempt at a solution

The only thing i could try is to square both sides but then this leads nowhere.

Any ideas??

Tedjn
Jun13-10, 10:49 PM
Start with the following inequalities: (Why are they true?)

0 ≤ (xy-1)(zw-1)
0 ≤ (x-1)(y-1)
0 ≤ (z-1)(w-1)

evagelos
Jun14-10, 05:41 AM
thanks!!!!