八年级数学题,都来帮忙想想啊
1〉若分式 x^2-2x+m分之1 不论x取何值总有意义,求m的取值范围
2〉若a b c为非零常数,且满足 c分之a+b-c=b分之a-b+c=a分之-a+b-c
又x=abc分之(a+b)(b+c)(a+c),且x<0.求x的值
参考答案:1〉若分式 x^2-2x+m分之1 不论x取何值总有意义,求m的取值范围
1/(x^2-2x+m)有意义,则:x^2-2x+m不=0
当:x^2-2x+m=0时
(x-1)^2=1-m>=0
m<=1
所以,M的取值范围是:m>1
2〉若a b c为非零常数,且满足 c分之a+b-c=b分之a-b+c=a分之-a+b-c
又x=abc分之(a+b)(b+c)(a+c),且x<0.求x的值
(a + b - c) / c = (a - b + c) / b = (-a + b + c) / a
(a+b)/c - 1 = (a+c)/b - 1 = (b+c)/a - 1
(a+b)/c = (a+c)/b = (b+c)/a
设 k = (a+b)/c = (a+c)/b = (b+c)/a
则:
ck = a + b
bk = a + c
ak = b + c
三式相加,得:(a+b+c)k = 2(a+b+c)
所以:a + b + c = 0,或 k = 2
① 若a + b + c = 0,则:
a+b = -c
b+c = -a
c+a = -b
k = (a+b)/c = -1
所以:x=(a+b)(b+c)(a+c) / abc = (-a)(-b)(-c) / abc = -1
② 若 k = 2,则:
x=(a+b)(b+c)(a+c) / abc
= [ (a+b)/c ] * [ (b+c)/a ] * [ (a+c)/b ]
= k^3 = 8
因x<0.所以第二个舍去,所以:X=-1