Có phải đề là:
\(E=\dfrac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\) (?)
\(=\dfrac{\left(\sqrt{a}\right)^3+\left(\sqrt{b}\right)^3}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=a-\sqrt{ab}+b-\sqrt{ab}\)
\(=a-2\sqrt{ab}+b\)
\(=\left(\sqrt{a}-\sqrt{b}\right)^2\)
#YM
\(E=\dfrac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=a-\sqrt{ab}+b-\sqrt{ab}\)
\(=a-2\sqrt{ab}+b=\left(\sqrt{a}-\sqrt{b}\right)^2\)
