- 58 名前：１３２人目の素数さん mailto:sage [2007/06/07(木) 21:58:46 ]
- >51 下
[B.3997]
x,y,z are real numbers. Prove that if xyz=u, then
x^4 + y^4 + z^4 + x^2･y^2 + y^2･z^2 + z^2･x^2 ≧ 2u(x+y+z).
(略解)
(左辺) - (右辺) = (1/2)(x^2 -y^2)^2 + (1/2)(y^2 -z^2)^2 + (1/2)(z^2 -x^2)^2
+ (x^2)(y-z)^2 + (y^2)(z-x)^2 + (z^2)(x-y)^2.
ハァハァ
