Algebra · Factorisation · Substitution · Systems of equations · Proportions
Let \(a\), \(b\), \(c\), \(d\), \(x\), \(y\) be positive real numbers such that
\[ a + 2ay + y = b + 2bx + x \qquad \text{and} \qquad x + 2xd + d = y + 2yc + c . \]
Prove that
\[ a + 2ad + d = b + 2bc + c . \]
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Serbian Republic Competition (Republicko takmicenje) 2000, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source