Giải thích các bước giải:
3x(x-11)=2x(x-8)
⇔ 3x²-33x=2x²-16x
⇔ 3x²-2x²-33x+16x=0
⇔ x²-17x=0
⇔ x(x-17)=0
⇔\(\left[ \begin{array}{l}x=0\\x-17=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x=17\end{array} \right.\)
Vậy x=0 hoặc x=17
(x-3)²=2x-6
⇔ x²-6x+9=2x-6
⇔ x²-6x-2x+9+6=0
⇔ x²-8x+15=0
⇔ x²-5x-3x+15=0
⇔ x(x-5)-3(x-5)=0
⇔ (x-3)(x-5)=0
⇔\(\left[ \begin{array}{l}x-3=0\\x-5=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=3\\x=5\end{array} \right.\)
Vậy x=3 hoặc x=5
(2x-3)²=(x-7)²
⇔ (2x-3)²-(x-7)²=0
⇔ (2x-3-x+7)(2x-3+x-7)=0
⇔ (x+4)(3x-10)=0
⇔\(\left[ \begin{array}{l}x+4=0\\3x-10=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-4\\3x=10\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-4\\x=10/3\end{array} \right.\)
Vậy x=-4 hoặc x=$\frac{10}{3}$
(x-1)(x+3)=(x+3)(2x+8)
⇔ (x-1)(x+3)-(x+3)(2x+8)=0
⇔ (x+3)(x-1-2x-8)=0
⇔ (x+3)(-x-9)=0
⇔ \(\left[ \begin{array}{l}x+3=0\\-x-9=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-3\\-x=9\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-3\\x=-9\end{array} \right.\)
Vậy x=-3 hoặc x=-9
(x+2)(x-5)=(3x-2)(3x-15)
⇔ (x+2)(x-5)=3(3x-2)(x-5)
⇔ (x+2)(x-5)-3(3x-2)(x-5)=0
⇔ (x-5)[(x+2)-3(3x-2)]=0
⇔ (x-5)[x+2-9x+6]=0
⇔ (x-5)[8-8x]=0
⇔ 8(x-5)[1-x]=0
⇔ (x-5)(1-x)=0
⇔\(\left[ \begin{array}{l}x-5=0\\1-x=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=5\\-x=-1\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=5\\x=1\end{array} \right.\)
Vậy x=5 hoặc x=1
