解不等式:(x-1)(x-2)(x-3)(x-4)>120

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解不等式:(x-1)(x-2)(x-3)(x-4)>120

解不等式:(x-1)(x-2)(x-3)(x-4)>120
解不等式:(x-1)(x-2)(x-3)(x-4)>120

解不等式:(x-1)(x-2)(x-3)(x-4)>120
=[(X-1)(X-4)][(X-2)(X-3)]-120
=[(X²-5X)+4][(X²-5X)+6]-120
=(X²-5X)²+10(X²-5X)+24-120
=(X²-5X)²+10(X²-5X)-96
=(X²-5X-6)(X²-5X+16)
=(X-6)(X+1)(X²-5X+16)>120
因为x^2-5x+16>0恒成立
所以x^2-5x-6>0
(x-6)(x+1)>0
x<-1或x>6

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