用配方法证明:(3x+1)(x-3)总是大于代数式x²-4x-9
问题描述：
用配方法证明:(3x+1)(x-3)总是大于代数式x²-4x-9
答
(3X+1)(X-3)-(X^2-4X-9)
=3X^2-8X-3-X^2+4X+9
=2X^2-4X+6
=2(X^2-2X+1)+4
=2(X-1)^2+4,
∵(X-1)^2≥0,
∴2(X-1)^2+4>0,
∴(3X+1)(X-3)>X^2-4X-9.