Algebra · Systems of equations · Factorisation · Symmetric systems
Find all real numbers \(a\), \(b\), \(c\), \(d\) for which
\[ \begin{aligned} abc + ab + bc + ca + a + b + c &= 2, \\ bcd + bc + cd + db + b + c + d &= 5, \\ cda + cd + da + ac + c + d + a &= 7, \\ dab + da + ab + bd + d + a + b &= 11. \end{aligned} \]
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Serbian Regional Competition (Okruzno takmicenje) 2000, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source