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Four real numbers with specified sum and sum of squares

Source: Czech-Polish-Slovak 2006 Q3

April 27, 2013
algebra unsolvedalgebra

Problem Statement

The sum of four real numbers is 99 and the sum of their squares is 2121. Prove that these numbers can be denoted by a,b,c,da, b, c, d so that ab−cd≥2ab-cd \ge 2 holds.
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