Đáp án + Giải thích các bước giải:
`a)` `(x-1)(x+2)-1=x^2+3`
`<=>x^2+2x-x-2-1-x^2-3=0`
`<=>x-6=0`
`<=>x=6`
Vậy `S={6}`
`b)` `(x-3)(x+3)-1=x^2+5`
`<=>x^2-9-1-x^2-5=0`
`<=>-15=0` ( vô lý)
Vậy `S=emptyset`
`c)` `(x-1)^2-x-1=0`
`<=>x^2-2x+1-x-1=0`
`<=>x^2-3x=0`
`<=>x(x-3)=0`
`<=>`\(\left[ \begin{array}{l}x=0\\x=3\end{array} \right.\)
Vậy `S={0;3}`
`d)` `x + x/2=1/3`
`<=>(6x)/6+(3x)/6=2/6`
`=>6x+3x=2`
`<=>9x=2`
`<=>x=2/9`
Vậy `S={2/9}`
`đ)` `2x^2-x-1=0`
`<=>2x^2-2x+x-1=0`
`<=>2x(x-1)+(x-1)=0`
`<=>(x-1)(2x+1)=0`
`<=>`\(\left[ \begin{array}{l}x=1\\x=-\dfrac{1}{2}\end{array} \right.\)
Vậy `S={1;-1/2}`.
`e)` `x^2-4x+3=0`
`<=>x^2-x-3x+3=0`
`<=>x(x-1)-3(x-1)=0`
`<=>(x-1)(x-3)=0`
`<=>`\(\left[ \begin{array}{l}x=1\\x=3\end{array} \right.\)
Vậy `S={1;3}`
