Đáp án:

 

Giải thích các bước giải:

 `0,5x(x-3)=(x-3)(1,5x-1)`

`<=>(x-3)(0,5x-1,5x+1)=0`

`<=>(x-3)(1-x)=0`

`=>x=3`

Hoặc `x=1`

`3x-15=2x(x-5)`

`<=>3(x-5)=2x(x-5)`

`<=>(x-5)(2x-3)=0`

`=>x=5`

Hoặc `x=3/2`

`(x^2-2x+1)-4=0`

`<=>(x-1)^2-4=0`

`<=>(x-3)(x+1)=0`

`=>x=3`

Hoặc `x=-1`

a) $0,5x(x-3)=(x-3)(1,5x-1)$

$↔ 0,5x(x-3)-(x-3)(1,5x-1)=0$

$↔ (x-3)(0,5x-1,5x+1)=0$

$↔ (x-3)(1-x)=0$

$↔ \left[ \begin{array}{l}x-3=0\\1-x=0\end{array} \right.$

$↔ \left[ \begin{array}{l}x=3\\x=1\end{array} \right.$

b) $3x-15=2x(x-5)$

$↔ 3(x-5)-2x(x-5)=0$

$↔ (x-5)(3-2x)=0$

$↔ \left[ \begin{array}{l}x-5=0\\3-2x=0\end{array} \right.$

$↔ \left[ \begin{array}{l}x=5\\x=\dfrac{3}{2}\end{array} \right.$

c) $(x^2-2x+1)-4=0$

$↔ (x-1)^2-2^2=0$

$↔ (x-1-2)(x-1+2)=0$

$↔ (x-3)(x+1)=0$

$↔ \left[ \begin{array}{l}x-3=0\\x+1=0\end{array} \right.$

$↔ \left[ \begin{array}{l}x=3\\x=-1\end{array} \right.$