(X-3)^2+(X^2-4X+3)^2=4咋解啊.

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 04:51:04
(X-3)^2+(X^2-4X+3)^2=4咋解啊.

(X-3)^2+(X^2-4X+3)^2=4咋解啊.
(X-3)^2+(X^2-4X+3)^2=4咋解啊.

(X-3)^2+(X^2-4X+3)^2=4咋解啊.
原式=(x-3)^2 *[(x-1)^2+1]=4.
由于(x-1)^2+1>=1,则x只可能取0,1,2.又由0

可将X^2-4X+3化简成(X-1)(x-3),设t=x-3;原式为t^2+t^2*(t+2)^2=4;提公因式t^2(t^2+4t+5)=4;又因为4只能分解成1*4或2*2.因此可猜的t等于-2;那么x等于1.

(x-3)^2+(x-3)^2(x-1)^2-4=0
x^2-6x+5+(x-3)^2(x-1)^2=0
(x-5)(x-1)+(x-3)^2(x-1)^2=0
(x-1)[(x-5)+(x-3)^2(x-1)]=0
x=1

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