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a + b + c + d = 2004, a^2 - b^2 + c^2 - d^2 =2004 2004 Romania District VIII p2

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August 15, 2024
algebrainequalities

Problem Statement

The real numbers a,b,c,da, b, c, d satisfy a>b>c>da > b > c > d and a+b+c+d=2004   and   a2−b2+c2−d2=2004.a + b + c + d = 2004 \,\,\, and \,\,\, a^2 - b^2 + c^2 - d^2 = 2004. Answer, with proof, to the following questions: a) What is the smallest possible value of aa? b) What is the number of possible values of aa?
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