17/07/14 10:25:53.58 54s0BI7v.net
>>66 下
a+b-c=z，b+c-a=x，c+a-b=y とおく。(*)
x,y,zは任意の正数。
a+b+c = x+y+z,
xy = cc-(a-b)^2 ≦ cc,
yz = aa-(b-c)^2 ≦ aa,
zx = bb-(c-a)^2 ≦ bb,
log（左辺）= a log(z）+ b log(x）+ c log(y)
= (y/2)log(yz) + (z/2)log(zx) + (x/2)log(xy)
≦ y log(a) + z log(b) + x log(c)
≦ a log(a) + b log(b) + c log(c) （←チェビシェフ）
= log（右辺）,