Giúp em với ạ. Em cảm ơn

Cho \(a,b,c\ge1\). CMR: 

\(a\left(b+c\right)+b\left(c+a\right)+c\left(a+b\right)+2\left(\dfrac{1}{a^2+1}+\dfrac{1}{b^2+1}+\dfrac{1}{c^2+1}\right)\ge9\)

Cho \(x,y,z\ge0,x+y+z=2\)

CMR: \(x^2y+y^2z+z^2x\le x^3+y^3+z^3\le1+\dfrac{1}{2}\left(x^4+y^4+z^4\right)\)

Cho a+b+c=0 . CMR :

\(8^a+8^b+8^c\ge2^a+2^b+2^c\)