(x-1)²-7(x-1)-8=0

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(x-1)²-7(x-1)-8=0
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(x-1)²-7(x-1)-8=0
(x-1)²-7(x-1)-8=0

(x-1)²-7(x-1)-8=0
(x-1)^2-7(x-1)-8=0
(x-1)^2-2x7/2(x-1)+(7/2)^2-8-(7/2)^2=0
(x-1-7/2)^2=8+49/4
(x-9/2)^2=81/4
x-9/2=±9/2
x=0或x=9

X1=0,X2=9

(x-1)²-7(x-1)-8=0
[(x-1)-8][(x-1)+1]=0
(x-9)x=0
x=9或x=0
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谢谢采纳

换元法,令(x-1)=t,再把它当做普通的一元二次方程处理,具体解法不用说了吧