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BALTIC-WAY 1999 Problem 1

  • Answer

Determine all real numbers a,b,c,da, b, c, d that satisfy the following system of equations.

{abc+ab+bc+ca+a+b+c=1bcd+bc+cd+db+b+c+d=9cda+cd+da+ac+c+d+a=9dab+da+ab+bd+d+a+b=9\left\{\begin{array}{r} a b c+a b+b c+c a+a+b+c=1 \\ b c d+b c+c d+d b+b+c+d=9 \\ c d a+c d+d a+a c+c+d+a=9 \\ d a b+d a+a b+b d+d+a+b=9 \end{array}\right.

Dataset text NuminaMath olympiads. Quoted with source.

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a=b=c=\sqrt[3]{2}-1, d=5 \sqrt[3]{2}-1

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