在下有请各位天才已知x²-4x+1=0,求代数式x²/(x-1)-1-1/x²-x的值千万不要死算啊……ps因为怕用高分悬赏但事后又无人回答,白白浪费了分.
问题描述：
在下有请各位天才
已知x²-4x+1=0,求代数式x²/(x-1)-1-1/x²-x的值
千万不要死算啊……
ps因为怕用高分悬赏但事后又无人回答,白白浪费了分.
答
4
答
把x²=4x-1代入化简
(4x-1)/(x-1)-1-1/(4x-1)-x
=4+3/(x-1)-1-1/(4x-1)-x
=3/(x-1)-1/(4x-1)-x+3
=(12x-3-x+1)/(x-1)(4x-1)-x+3
=(11x-2)/(4x²-5x+1)-x+3
=(11x-2)/(-x)-x+3
=-11+2/x-x+3
=2/x-x-8
然后求解X,再代入计算。
答
x²+1=4x(x²+1)/x=4原式=x²/(x-1)-1-1/x(x-1)=[x³-x(x-1)-1]/x(x-1)=(x³-x²+x-1)/x(x-1)=[x²(x-1)+(x-1)]/x(x-1)=(x²+1)(x-1)/x(x-1)=(x²+1)/x=4
答
x²/(x-1)-1-1/x²-x
=（x³-x²+x-1)/(x²-x)
=(x-1)(x²+1）/x(x-1)
=(x²+1）/x
=x+1/x
由x²-4x+1=0两边同时除以x，得
x-4+1/x=0
∴x+1/x=4
∴原式=4