1)
Ta có:
\(\dfrac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=\dfrac{\left(\sqrt{a}\right)^3+\left(\sqrt{b}\right)^3}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=a-\sqrt{ab}+b-\sqrt{ab}\)
\(=a-2\sqrt{ab}+b\)
\(=\left(\sqrt{a}-\sqrt{b}\right)^2\)
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1: \(\dfrac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=a-2\sqrt{ab}+b\)
\(=\left(\sqrt{a}-\sqrt{b}\right)^2\)
4: \(\left(1+\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\right)\left(1-\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)
\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)\)
=1-a
Đúng 2
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