Giải thích các bước giải:
Bài 1:
Ta có :
$M=\dfrac{bc}{a^2(b+c)}+\dfrac{ca}{b^2(a+c)}+\dfrac{ab}{c^2(a+b)}$
$\rightarrow M=\dfrac{(\dfrac{1}{a})^2}{\dfrac{1}{b}+\dfrac{1}{c}}+\dfrac{(\dfrac{1}{b})^2}{\dfrac{1}{c}+\dfrac{1}{a}}+\dfrac{(\dfrac{1}{c})^2}{\dfrac{1}{a}+\dfrac{1}{b}}$
$\rightarrow M\ge\dfrac{(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c})^2}{\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{1}{c}+\dfrac{1}{a}+\dfrac{1}{a}+\dfrac{1}{b}}$
$\rightarrow M\ge\dfrac{(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c})^2}{2(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c})}$
$\rightarrow M\ge\dfrac{1}{2}.(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c})$
$\rightarrow M\ge\dfrac{1}{2}.(3\sqrt[3]{\dfrac{1}{a}.\dfrac{1}{b}.\dfrac{1}{c}})$
$\rightarrow M\ge \dfrac{3}{2}$
Dấu = xảy ra khi $a=b=c=1$