Đáp án:
Phía dưới
Giải thích các bước giải:
` a)5(x+3)-2x(3+x)=0`
`⇔(5-2x)(x+3)=0`
`⇔`\(\left[ \begin{array}{l}5-2x=0\\x+3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=\dfrac{5}{2}\\x=-3\end{array} \right.\)
Vậy `x=5/2` hoặc `x=-3`
`b) (x+2)(x-3)-3x+9=0`
`⇔(x+2)(x-3)-3(x-3)=0`
`⇔(x+2-3)(x-3)=0`
`⇔(x-1)(x-3)=0`
`⇔`\(\left[ \begin{array}{l}x-1=0\\x-3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=1\\x=3\end{array} \right.\)
Vậy `x=1` hoặc` x=3`
`c)(x-3)^2-(2x+1)(3-x)=x(3-x)`
`⇔(x-3)^2+(2x+1)(x-3)+x(x-3)=0`
`⇔(x-3)(x-3+2x+1+x)=0`
`⇔(x-3)(4x-2)=0`
`⇔`\(\left[ \begin{array}{l}x-3=0\\4x-2=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=3\\x=\dfrac{1}{2}\end{array} \right.\)
Vậy `x=3` hoặc `x=1/2`
`d) 4(x-4)^2-121=0`
`⇔(2x-8)^2-11^2=0`
`⇔(2x-8-11)(2x-8+11)=0`
`⇔(2x-19)(2x+3)=0`
`⇔`\(\left[ \begin{array}{l}2x-19=0\\2x+3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=\dfrac{19}{2}\\x=-\dfrac{3}{2}\end{array} \right.\)
Vậy `x=19/2 `hoặc `x=-3/2`
`e) 9(x-1)^2-16(x+5)^2=0`
`⇔(3x-3)^2-(4x+20)^2=0`
`⇔(3x-3-4x-20)(3x-3+4x+20)=0`
`⇔(-x-23)(7x+17)=0`
`⇔`\(\left[ \begin{array}{l}-x-23=0\\7x+17=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=-23\\x=-\dfrac{17}{7}\end{array} \right.\)
Vậy `x=-23` hoặc `x=-17/7`
