Cho a,b,c>0. CMR với mọi a,b,c thì \(\dfrac{a^2+bc}{b+c}+\dfrac{b^2+ca}{c+a}+\dfrac{c^2+ab}{a+b}\ge a+b+c\)

Cho a,b,c >0 thỏa mãn abc=1.CMR \(\dfrac{a^3}{\left(1+b\right)\left(1+c\right)}+\dfrac{b^3}{\left(1+c\right)\left(1+a\right)}+\dfrac{c^3}{\left(1+a\right)\left(1+b\right)}\ge\dfrac{3}{4}\)

Cho x,y,z>0 x+y+z=1. CMR \(x^2+y^2+z^2+2\sqrt{3xyz}\le1\)