04/11/24 01:51:26
>>647 (続き)
(6) [1993 Poland] 44th, 2nd roud, 1st day No.1 (1993.2)
S=a+b+c+d, U=bcd+cda+dab+abc とおく。
左辺 - 右辺 = (a+c)(b+d)/S -ab/(a+b) -cd/(c+d)
= [(a+c)(b+d)(a+b)(c+d)-SU]/[S(a+b)(c+d)] = (ad-bc)^2 /[S(a+b)(c+d)] ≧0.
(7) b/c=x, c/a=y, a/b=z とおくと u=xyz=1.
左辺 = x/(y+1) +y/(z+1) +z/(x+1) = [3u +(s^2 -2t) +t +s]/[(x+1)(y+1)(z+1)].
右辺 = 1/(y+1) +1/(z+1) +1/(x+1) = (t+2s+3)/[(x+1)(y+1)(z+1)].
[左辺－右辺]･(x+1)(y+1)(z+1) = (s^2 -2t) -s
= (1/2)[(x^2 +y^2 +z^2 -3) +(x-1)^2 +(y-1)^2 +(z-1)^2] ≧0.
ぬるぽ