Ta có \(VT = \dfrac{{a\sqrt a + b\sqrt b }}{{\sqrt a + \sqrt b }} - \sqrt {ab} \\ = \dfrac{{{{\left( {\sqrt a } \right)}^3} + {{\left( {\sqrt b } \right)}^3}}}{{\sqrt a + \sqrt b }} - \sqrt {ab} \) \( = \dfrac{{\left( {\sqrt a + \sqrt b } \right)\left( {a - \sqrt {ab} + b} \right)}}{{\sqrt a + \sqrt b }} - \sqrt {ab} \) \( = a - \sqrt {ab} + b - \sqrt {ab} \\= {\left( {\sqrt a } \right)^2} - 2\sqrt {ab} + {\left( {\sqrt b } \right)^2}\) \( = {\left( {\sqrt a - \sqrt b } \right)^2} = VP\) (đpcm).
