Question

[Nguyễn Thị Thu Hằng]

Tính giá trị biểu thức

\(\frac{a\sqrt{a}-b\sqrt{b}}{\sqrt{a}-\sqrt{b}}\) \(\left(a\ge0;b\ge0;a\ne b\right)\)

Answer 1

[svtkvtm]

\(\frac{a\sqrt{a}-b\sqrt{b}}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt{a^3}-\sqrt{b^3}}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}\right)^3-\left(\sqrt{b}\right)^3}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}{\sqrt{a}-\sqrt{b}}=a+\sqrt{ab}+b\)