Last edited by hbghlyj 2020-11-21 19:02$n\inN$,设$E ( a , b , c ) = a ( a - b ) ( a - c ) + b ( b - c ) ( b - a ) + c ( c - a ) ( c - b ) $,求最小的k,使$\left(\sum a^{2n-1}\right)E\left(a,b,c\right)\ge k\sum{a^nb^n\left(a-b\right)^2}$对任意正数a,b,c恒成立
n=0,$k=\frac{1}{2}$,当且仅当(a,b,c)~(1,1,1)时取等.
n=1,k=1,当且仅当(a,b,c)~(1,1,1)或(0,1,1)时取等.
n=2,$k=\frac{3}{2}$,当且仅当(a,b,c)~(1,1,1)或(0,1,1)时取等.
PS:赞word2019自带的latex公式编辑器，直接复制出来就是latex. |
