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1/(x ^ 2+y+z) +1/(x+y^2+z) + 1/(x+y+z^2) <=1, if x+y+z=3, x,y,z >=0

Source: Tuymaada Junior 2006 p4

May 12, 2019
algebrainequalitiesthree variable inequality

Problem Statement

The sum of non-negative numbers x x , y y and z z is 33. Prove the inequality 1x2+y+z+1x+y2+z+1x+y+z2≤1. {1 \over x ^ 2 + y + z} + {1 \over x + y ^ 2 + z} + {1 \over x + y + z ^ 2} \leq 1.
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