08/07/19 00:09:16
>>392
(1) 基本対称式を x+y+z =s, xy+yz+zx =t, xyz =u とおく。
{x(y-1)(z-1)}^2 + {(x-1)y(z-1)}^2 + {(x-1)(y-1)z}^2 - {(x-1)(y-1)(z-1)}^2
= 3u^2 -4tu +2t^2 -2(st-3u) + (s^2 -2t) - (u-t+s-1)^2
= (t-3)^2 + 2(u-1)(u-t-s+5),
= (t-3)^2 (← 題意より u=1)
≧ 0,
これを {(x-1)(y-1)(z-1)}^2 >0 で割る。
(2) 等号条件は t=3, u=1. なので･･･