Bài 2:
$(\sqrt{a}-\sqrt{b})\ge 0$ (luôn đúng)
$\Leftrightarrow a-2\sqrt{ab}+b\ge 0$
$\Leftrightarrow a+b\ge 2\sqrt{ab}$ (*)
Dấu "=" xảy ra khi $a=b=0$
Bài 3:
Xét $2a+2b+2c= (a+b)+(b+c)+(a+c)$
Theo (*):
$a+b\ge 2\sqrt{ab}$
$b+c\ge 2\sqrt{bc}$
$c+a\ge 2\sqrt{ca}$
$\Rightarrow 2a+2b+2c\ge 2\sqrt{ab}+2\sqrt{bc}+2\sqrt{ca}$
$\Leftrightarrow a+b+c\ge \sqrt{ab}+\sqrt{bc}+\sqrt{bc}$
Dấu "=" xảy ra khi $a=b=c=0$
Bài 4:
$\frac{x+1}{\sqrt{x}}=\sqrt{x}+\frac{1}{\sqrt{x}} \ge 2\sqrt{\sqrt{x}.\frac{1}{\sqrt{x}}}=2$
Dấu "=" xảy ra khi $x=1$
