olymmath

JBMO-SL 2010 A1

    The real numbers a,b,c,da, b, c, d satisfy simultaneously the equations

    abc−d=1,bcd−a=2,cda−b=3,dab−c=−6a b c-d=1, b c d-a=2, c d a-b=3, d a b-c=-6

    Prove that a+b+c+d≠0a+b+c+d \neq 0.

    Dataset text NuminaMath olympiads. Quoted with source.

    Also JBMO 2010 Problem 1.

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