Algebra · Systems of equations · Homogeneous quadratics · Sign constraints
Let \(t\) be a real number and let \(a\) and \(b\) be positive real numbers satisfying
\[ 2a^2 - 3abt + b^2 \;=\; 2a^2 + abt - b^2 \;=\; 0 . \]
Determine the value of \(t\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2010, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source