\(\frac{2a}{b+c}+\frac{b+c}{2a}\ge2\sqrt{\frac{2a\left(b+c\right)}{\left(b+c\right)2a}}=2\)
Dấu "=" xảy ra khi \(2a=b+c\)
\(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=\frac{a^2}{ab+ac}+\frac{b^2}{bc+ab}+\frac{c^2}{ac+bc}\ge\frac{\left(a+b+c\right)^2}{2\left(ab+bc+ca\right)}\ge\frac{3\left(ab+bc+ca\right)}{2\left(ab+bc+ca\right)}=\frac{3}{2}\)
Dấu "=" xảy ra khi \(a=b=c\)