Giải các phương trình:

$$\begin{gathered} a) (x^2-2x+1)-4=0 \\ b) x^2-x=-2x+2 \\ c) 4x^2+4x+1=x^2 \\ d) x^2-5x+6=0 \end{gathered}$$

Giải

$$\begin{gathered} a) (x^2-2x+1)-4=0\iff {(x-1)}^2-2^2=0 \\ \iff \left[(x-1)+2\right]\left[(x-1)-2\right]=0 \\ \iff (x+1\left)\right(x-3)=0\Rightarrow S=\left[-1;3\right] \\ b) x^2-x=-2x+2\iff x(x-1)-2(x-1)=0 \\ \iff (x-1)(x+2)=0\Rightarrow S=\left[-2;1\right] \\ c) 4x^2+4x+1=x^2\iff {(2x+1)}^2-x^2=0 \\ \iff (3x+1\left)\right(x+1)=0\Rightarrow S=\left\{-1;-\frac{1}{3}\right\} \\ d. x^2-5x+6=0\iff x(x-2)-3(x-2)=0 \\ \iff (x-2\left)\right(x-3)=0\Rightarrow S=\left[2;3\right] \end{gathered}$$