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sum \sqrt{xy +1}> x+ y + z - All-Russian MO 2004 Regional (R4) 9.6

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September 27, 2024
algebrainequalities

Problem Statement

Positive numbers x,y,zx, y, z are such that the absolute value of the difference of any two of them are less than 22. Prove that xy+1+yz+1+zx+1>x+y+z. \sqrt{xy +1}+\sqrt{yz + 1}+\sqrt{zx+ 1} > x+ y + z.
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