比较(x+1)(x²-x+2)与(x-1)(x²+x+2)的大小

比较(x+1)(x²-x+2)与(x-1)(x²+x+2)的大小
比较(x+1)(x²-x+2)与(x-1)(x²+x+2)的大小

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)

(x+1)(x²-x+2)
=(x+1)(x²-x+1+1)
=(x+1)(x²-x+1)+(x+1)
=x³+1+x+1
=x³+x+2
(x-1)(x²+x+2)
=(x-1)(x²+x+1+1)
=(x-1)(x²+x+1)+(x-1)
=x³-1+x-1
=x³+x-2
因为：x³+x+2＞x³+x-2
所以，(x+1)(x²-x+2)＞(x-1)(x²+x+2)