04/08/21 10:15
>339
左辺 = (a^2)bc + a(b^2)c + ab(c^2) = (a+b+c)abc
= (1/27)(a+b+c){(a+b+c)^3 -3a(b-c)^2 -3b(c-a)^2 -3(a-b)^2} ≦ (1/27)(a+b+c)^4,
(a+b+c)^2 = 3(a^2+b^2+c^2) -(b-c)^2 -(c-a)^2 -(a-b)^2 ≦ 3(a^2+b^2+c^2).
04/08/21 10:15
>339
左辺 = (a^2)bc + a(b^2)c + ab(c^2) = (a+b+c)abc
= (1/27)(a+b+c){(a+b+c)^3 -3a(b-c)^2 -3b(c-a)^2 -3(a-b)^2} ≦ (1/27)(a+b+c)^4,
(a+b+c)^2 = 3(a^2+b^2+c^2) -(b-c)^2 -(c-a)^2 -(a-b)^2 ≦ 3(a^2+b^2+c^2).