Đáp án + Giải thích các bước giải:
`a)` `(2x-1)(x-3)+4x^2=1`
`<=>2x^2-6x-x+3+4x^2=1`
`<=>6x^2-7x+3-1=0`
`<=>6x^2-7x+2=0`
`<=>6x^2-3x-4x+2=0`
`<=>3x(2x-1)-2(2x-1)=0`
`<=>(2x-1)(3x-2)=0`
`<=>` \(\left[ \begin{array}{l}2x-1=0\\3x-2=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=\dfrac{2}{3}\end{array} \right.\)
Vậy `S={1/2;2/3}`
`b)` `x^3-4x^2-x+4=0`
`<=>x^2(x-4)-(x-4)=0`
`<=>(x-4)(x^2-1)=0`
`<=>(x-4)(x-1)(x+1)=0`
`<=>[(x-4=0),(x-1=0),(x+1=0):}`
`<=>[(x=4),(x=1),(x=-1):}`
Vậy `S={4;1;-1}`
`c)` `3x^2-5x-8=0`
`<=>3x^2+3x-8x-8=0`
`<=>3x(x+1)-8(x+1)=0`
`<=>(x+1)(3x-8)=0`
`<=>`\(\left[ \begin{array}{l}x+1=0\\3x-8=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-1\\x=\dfrac{8}{3}\end{array} \right.\)
Vậy `S={-1;8/3}`.
