比较(x+1)(x²-x+2)与(x-1)(x²+x+2)的大小

问题描述:

比较(x+1)(x²-x+2)与(x-1)(x²+x+2)的大小

(x+1)(x²-x+2)-(x-1)(x²+x+2)=[(x+1)(x²-x+1)+(x+1)]-[(x-1)(x²+x+1)+(x-1)]=(x³+1+x+1)-(x³-1+x-1)=4>0∴(x+1)(x²-x+2)>(x-1)(x²+x+2)