Prove that (1) A, b and c are positive numbers,

So a+b≥2ab, b+c≥2bc, c+a≥2ca?

A+bb+cc+a≥8a2b2c2？ , that is, a+bb+cc+a≥8abc?

When a=b=c, the equal sign holds.

Because a, b and c are not all equal positive numbers, a+a+b b+ cc+a >；; 8abc？

(2) a+b≥2ab，b+c≥2bc，c+a≥2ca？

Add the three formulas to get 2a+2b+2c≥2ab+2bc+2ca? , that is, a+b+c≥ab+bc+ca?

When a=b=c, the equal sign holds.

Because a, b and c are not all equal positive numbers, a+b a+b+c >；; ab+bc+ca？ .