MathCastle
Proof Writing & Problem SolvingEasy

Proof Writing & Problem Solving · Easy problem

A direct proof that a+b2≥ab\dfrac{a + b}{2} \ge \sqrt{ab} for a,b≥0a, b \ge 0 uses the identity a+b2−ab=(a−b)22\dfrac{a + b}{2} - \sqrt{ab} = \dfrac{(\sqrt a - \sqrt b)^2}{2}. For a=4a = 4 and b=9b = 9, what is a+b2−ab\dfrac{a + b}{2} - \sqrt{ab}?

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