Đáp án:
1) `7x(x-4)-x+4 = 0`
`⇔ 7x(x-4)-(x-4) = 0`
`⇔ (x-4)(7x-1) = 0`
⇔\(\left[ \begin{array}{l}x-4=0\\7x-1=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=4\\x=\frac{1}{7}\end{array} \right.\)
2) `x^3-3x^2+x-3=0`
`⇔ (x^3-3x^2)+(x-3)=0`
`⇔ x^2(x-3)+(x-3) = 0`
`⇔ (x-3)(x^2+1) = 0`
`⇔ x-3 = 0 (vỉ x^2+1 > 0)`
`⇔ x = 3`
3) `x^3-2x^2-9x+18=0`
`⇔ (x^3-2x^2)-(9x-18)=0`
`⇔ x^2(x-2)-9(x-2) = 0`
`⇔ (x-2)(x^2-9) = 0`
`⇔ (x-2)(x-3)(x+3) = 0`
⇔\(\left[ \begin{array}{l}x-2=0\\x-3=0;x+3=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=2\\x=3;x=-3\end{array} \right.\)
4) `3x(x-1)+x-1=0`
`⇔ 3x(x-1)+(x-1)=0`
`⇔ (x-1)(3x+1) = 0`
⇔\(\left[ \begin{array}{l}x-1=0\\3x+1=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=1\\x=\frac{-1}{3}\end{array} \right.\)
5) `2(x+3)-x^2-3x=0`
`⇔ 2(x+3)-(x^2+3x)=0`
`⇔ 2(x+3)-x(x+3) = 0`
`⇔ (x+3)(2-x)`
⇔\(\left[ \begin{array}{l}x+3=0\\2-x=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-3\\x=2\end{array} \right.\)
6) `6x^2-15x-(2x-5)(x+5)=0`
`⇔ (6x^2-15x)-(2x-5)(x+5)=0`
`⇔ 3x(2x-5)-(2x-5)(x+5)=0`
`⇔ (2x-5)[3x-(x+5)] = 0`
`⇔ (2x-5)(3x-x-5) = 0`
`⇔ (2x-5)(2x-5) = 0`
`⇔ (2x-5)^2 = 0`
`⇔ 2x-5 = 0`
`⇔ 2x = 5`
`⇔ x = 5/2`
