阅读下列内容后,解答下列各题:几个不等于0的数相乘,积的符号由负因数的个数决定.
例如:考查代数式(x-1)(x-2)的值与0的大小.
当x<1时,x-1<0,x-2<0,∴(x-1)(x-2)>0
当1<x<2时,x-1>0,x-2<0,∴(x-1)(x-2)<0
当x>2时,x-1>0,x-2>0,
综上:当1<x<2时,(x-1)(x-2)<0;当x<1或x>2时,(x-1)(x-2)>0
阅读下表:
由表可知,当x满足 时,(x+2)(x+1)(x-3)<0
运用你发现的规律,写出当x满足 时,(x+6)(x-7)(x+8)(x-9)<0.
0 163919 163927 163933 163937 163943 163945 163949 163955 163957 163963 163969 163973 163975 163979 163985 163987 163993 163997 163999 164003 164005 164009 164011 164013 164014 164015 164017 164018 164019 164021 164023 164027 164029 164033 164035 164039 164045 164047 164053 164057 164059 164063 164069 164075 164077 164083 164087 164089 164095 164099 164105 164113 366461
例如:考查代数式(x-1)(x-2)的值与0的大小.
当x<1时,x-1<0,x-2<0,∴(x-1)(x-2)>0
当1<x<2时,x-1>0,x-2<0,∴(x-1)(x-2)<0
当x>2时,x-1>0,x-2>0,
综上:当1<x<2时,(x-1)(x-2)<0;当x<1或x>2时,(x-1)(x-2)>0
阅读下表:
| x<-2 | -2<x<-1 | -1<x<3 | x>3 | |
| x+2 | - | + | + | + |
| x+1 | - | - | + | + |
| x-3 | - | - | - | + |
运用你发现的规律,写出当x满足 时,(x+6)(x-7)(x+8)(x-9)<0.