Question

x²-2x-4|x-1|+5=0

用换元法解方程

Answer 1

x^2-2x-4|x-1|+5=0
case 1: x≥1
x^2-2x-4|x-1|+5=0
x^2-2x-4(x-1)+5=0
x^2-6x+9=0
(x-3)^2 =0
x=3
solution for case 1: x=3
case 2: x<0
x^2-2x-4|x-1|+5=0
x^2-2x+4(x-1)+5=0
x^2+2x+1=0
(x+1)^2 =0
x=-1
solution for case 2: x=-1
ie
x^2-2x-4|x-1|+5=0
x=3 or -1

Answer 2

原方程可以转化为(x-1)^2-4|x-1|+4=0，或|x-1|^2-4|x-1|+4=0，得到(|x-1|-2)^2=0，令t=|x-1|，则有(t-2)^2=0一>t=2，即|x-1|=2，继续解得x=-1或x=3。