Question

试比较（x²-x+1）(x²+x+1)与(x²-x+1)(x²+x+1).

Answer 1

解：(x²-x+1)(x²+x+1)-(x²-x+1)(x²+x+1)

=［(x²+1)²-(x)²］-［（x²+1）²-x²］

=-x².

当x≠0时，-x²＜0,（x²-x+1）(x²+x+1)＜(x²-x+1)(x²+x+1);

当x=0时,-x²=0,（x²-x+1）(x²+x+1)=(x²-x+1)(x²+x+1).