(x²-2x)²+2(x²-2x)+1怎么解

问题描述:

(x²-2x)²+2(x²-2x)+1
怎么解

(x²-2x)²+2(x²-2x)+1
=[(x²-2x) +1]^2
=[x²-2x +1]^2

设t=x²-2x
原式=t²+2t+1
=(t+1)²
=(x²-2x+1)²
=(x-1)的四次方

(x²-2x)²+2(x²-2x)+1
=(x²-2x+1)²
=[(x+1)²]²
=(x+1)^4

(x²-2x)²+2(x²-2x)+1
=(x²-2x+1)²
=[(x+1)²]²
=(x+1)^4

(x²-2x)²+2(x²-2x)+1
=[(x²+2x)+1]²
=(x²+2x+1)²
=[(x+1)²]²
=(x+1)^4