谁能解不等式(x-1)(x-2)(x-3)(x-4)》24?
问题描述:
谁能解不等式(x-1)(x-2)(x-3)(x-4)》24?
答
[(x-1)(x-4)][(x-2)(x-3)]>24[(x^2-5x)+4][(x^2-5x)+6]>24(x^2-5x)^2+10(x^2-5x)+24>24(x^2-5x)^2+10(x^2-5x)>0(x^2-5x)(x^2-5x+10)>0因为x^2-5x+10=(x-5/2)^2+15/4>0所以x^2-5x>0x(x-5)>0x5