Question

比较(x+1)(x²-x+2)与(x-1)(x²+x+2)的大小

Answer 1

(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)