Đáp án+Giải thích các bước giải:
Bài `4:`
`1) 3x(x-7)+2x-14=0`
`<=> 3x(x-7)+2(x-7)=0`
`<=> (x-7).(3x+2)=0`
`<=>`\(\left[ \begin{array}{l}x-7=0\\3x+2=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=7\\3x=-2\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=7\\x=\dfrac{-2}{3}\end{array} \right.\)
Vậy `x∈{7; -2/3}`
`2) x^3+3x^2-(x+3)=0`
`<=> x^2(x+3)-(x+3)=0`
`<=> (x^2-1)(x+3)=0`
`<=> (x-1)(x+1)(x+3)=0`
`<=>`\(\left[ \begin{array}{l}x-1=0\\x+1=0\\x+3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=1\\x=-1\\x=-3\end{array} \right.\)
Vậy `x∈{±1; -3}`
`3) (4-x)^2-16=0`
`<=> (4-x)^2-4^2=0`
`<=> (4-x-4).(4-x+4)=0`
`<=> -x . (8-x)=0`
`<=> `\(\left[ \begin{array}{l}-x=0\\8-x=0\end{array} \right.\)
`<=> `\(\left[ \begin{array}{l}x=0\\x=8\end{array} \right.\)
Vậy `x∈{0; 8}`
`4) 25-(3-x)^2=0`
`<=> 5^2-(3-x)^2=0`
`<=> (5-3+x).(5+3-x)=0`
`<=> (2+x)(8-x)=0`
`<=>`\(\left[ \begin{array}{l}2+x=0\\8-x=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-2\\x=8\end{array} \right.\)
Vậy `x∈{-2; 8}`
