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