对任意实数x,比较大小(x-2)(x+6)与(x-1)(x-3)

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对任意实数x,比较大小(x-2)(x+6)与(x-1)(x-3)

对任意实数x,比较大小(x-2)(x+6)与(x-1)(x-3)
对任意实数x,比较大小(x-2)(x+6)与(x-1)(x-3)

对任意实数x,比较大小(x-2)(x+6)与(x-1)(x-3)
(x-2)(x+6)-(x-1)(x-3)
=(x²+4x-12)-(x²-4x+3)
=x²+4x-12-x²+4x-3
=8x-15
x>15/8时,8x-15>0 (x-2)(x+6)>(x-1)(x-3)
x=15/8时,8x-15=0 (x-2)(x+6)=(x-1)(x-3)
x


因为(x-2)(x+6)-(x-1)(x-3)
=x²+4x-12-(x²-4x+3)
=8x-15
所以
当x≥15/8时,(x-2)(x+6)≥(x-1)(x-3)
当x<15/8时,(x-2)(x+6)<(x-1)(x-3)

(x-2)(x+6)-(x-1)(x-3)
=X^2+4X-12-(X^2-4X+3)
=8X-15
当X>15/8时
(x-2)(x+6)-(x-1)(x-3)>0
(x-2)(x+6)>(x-1)(x-3)
当X=15/8时
(x-2)(x+6)-(x-1)(x-3)=0
(x-2)(x+6)=(x-1)(x-3)
当X<15/8时
(x-2)(x+6)-(x-1)(x-3)<0
(x-2)(x+6)<(x-1)(x-3)