淘宝那个类目产品冷门:初一数学,大家帮帮忙

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1.当m、n为何值时,等式(3x-4)/(x^2-3x+2)=m/(x-1)+n/(n+2)总能成立。
2.已知x^2-4x+1=0,求(1)x=1/x (2)x^2+1/x^2 (3)x^3+1/x^3 (4)x^4+1/x^4的值

要详细解题过程

1.是n/(x-2)吧
(3x-4)/(x^2-3x+2)=m/(x-1)+n/(x-2)
(3x-4)/(x-1)(x-2)=m/(x-1)+n/(x-2)
3x-4=m(x-2)+n(x-1)
3x-4=(m+n)x-2m-n
m+n=3
2m+n=4
m=1,n=2

2.
(1)
x^2-4x+1=0
x-4+1/x=0
x+1/x=4

(2)
x^2+1/x^2
=(x+1/x)^2-2
=14

(3)
x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
=4*13
=52

(4)
x^4+1/x^4
=(x^2+1/x^2)^2-2
=194