Question

chứng minh : \(\left(\dfrac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}}-\sqrt{ab}\right):\left(a-b\right)+\dfrac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}=1\)

Answer 1

\(\left(\dfrac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right):\left(a-b\right)+\dfrac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}=1\)

\(VT=\dfrac{\left(a-\sqrt{ab}+b-\sqrt{ab}\right)}{a-b}+\dfrac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)

\(=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{a-b}+\dfrac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)

\(=\dfrac{\sqrt{a}-\sqrt{b}+2\sqrt{b}}{\sqrt{a}+\sqrt{b}}=1=VP\)