Algebra · Algebraic identity · Fractions · Arithmetic progression
Let \(a\), \(b\), \(c\) be positive numbers with \(a^2 + c^2 = 2b^2\). Prove that
\[ \frac{2}{a+c} = \frac{1}{a+b} + \frac{1}{b+c} . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2003, 1. letnik, category A, problem 3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source