对于任意实数x(详见问题22)

(1)证明:

2x?+4x+3

=2(x?+2x)+3

=2(x?+2x+1)+3-2

=2(x+1)?+1

∫(x+1)?≥0

∴2(x+1)?+1>0

那么对于任意实数,2x?+4x+3>0

(2)证明:

(3x?-5x-1)-(2x?-4x 7)

=3x?-5x-1-2x?+4x+7

=x?-x+6

=(x?-x+1/4)+7-1/4

=(x-1/2)?+27/4

∫(x-1/2)?≥0

∴(x-1/2)?+27/4>0

那么不管x是什么,多项式3x?-5x-1的值总是大于2x?-4x-3