Algebra · Constrained inequalities · Symmetric substitution · Equality cases
Let \(x\) and \(y\) be nonnegative real numbers with \(x + y = 2\). Prove that
\[ x^2 y^2 \left( x^2 + y^2 \right) \leq 2 . \]
When does equality hold?
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Serbian Republic Competition (Republicko takmicenje) 2003, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source