Question

Gấp gấp

Answer 1

1,  đk a ; b > 0 

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

\(=\dfrac{4\sqrt{ab}}{2\left(a-b\right)}+\dfrac{-4\sqrt{ab}}{2\left(ab\right)}=0\)

2, đk a ; b > 0 

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

\(=\dfrac{\left(a-b\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}\left(\sqrt{a}-\sqrt{b}\right)^2=\left(\sqrt{a}-\sqrt{b}\right)^4\)

3,đk a ; b > 0 

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