(1)
A = aa -bb +3bc,
B = bb -cc +3ca,
C = cc -aa +3ab,
とおくと
(左辺) - (右辺) = {(A-B)^2 + (B-C)^2 + (C-A)^2}/6 ≧ 0,
>>244 (1) >>247
(2) AM-GMで
{23(a^4)b +7(b^4)c +11(c^4)d +10(d^4)a}/51 ≧ a(abcd) = a,
巡回的にたす。
(3)
右)
(中辺) = 1 - 2abc/{(a+b)(b+c)(c+a)} < 1,
左)
(中辺) - 3/4 = {(a+b)(b+c)(c+a)-8abc}/(a+b)(b+c)(c+a) ≧ 0, (AM-GM)
