题目设a,b,c是三个实数,证明:(1)a~4+b~4+c~4+ab~3+bc~3+ca~3≥2(a~3b+b~3c+c~3a);(2)(a~2+b~2+c~2)2≥3(a~3b+b~3c+c~3a).这是文献[1]、[2]所介绍的不等式,除[2]中用全导数方法给出了两个不等式的证明外,书[1]还用(多种)配方法(或判别式法)给出了以上两式的证明,并指出等号成立的条件(在a≥b≥c的前提下):除了平凡情况a=b=c之外,不等式(1)等号成立的 The problem is that a, b, c are three real numbers, which prove that: a ~ 4 + b ~ 4 + c ~ 4 + ab ~ 3 + bc ~ 3 + ca ~ 3≥2 (a ~ 3b + b ~ 3c (2) (a ~ 2 + b ~ 2 + c ~ 2) 2≥3 (a ~ 3b + b ~ 3c + c ~ 3a) This is literature [1], [2] In addition to the inequalities introduced in [2], two proofs of the inequalities are given in [2], and the book [1] gives the proof of the above two formulas by the method (or discriminant method) And pointed out that the condition of equal sign (under the condition of a ≥ b ≥ c): except for the ordinary case a = b = c, the inequality (1) equals