Đáp án+Giải thích các bước giải:
Bài `3;`
`a) x^2 -x=0`
`<=> x(x-1)=0`
`<=>`\(\left[ \begin{array}{l}x=0\\x-1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\x=1\end{array} \right.\)
Vậy `x in {0; 1}`
`b) (x+1)^2 -x = -1`
`<=> (x+1)^2 -x +1=0`
`<=> x^2 +2x + 1 -x +1=0`
`<=> x^2 + x +2=0`
`<=> x^2 +2.x . 1/2 + 1/4 + 7/4 =0`
`<=> (x+1/2)^2 = -7/4`(vô nghiệm)
Vậy `x ∈ ∅`
`c) 3x^2 - 2x(x-1) = x(x+1)`
`<=> 3x^2 - 2x(x-1) - x(x+1)=0`
`<=> x[3x - 2(x-1) -(x+1)]=0`
`<=> x(3x - 2x + 2 -x -1)=0`
`<=> x.1=0`
`<=> x =0`
Vậy `x in {0}`
`d) x^2(x-1) +4x=4`
`<=> x^2(x-1) +4x-4=0`
`<=> x^2(x-1)+4(x-1)=0`
`<=> (x^2+4)(x-1)=0`
`<=> x-1=0(` vì `x^2 + 4 > 0 ∀x)`
`<=> x =1`
`e) x^2 - x =6`
`<=> x^2 -x - 6=0`
`<=> x^2 +2x- 3x - 6=0`
`<=> x(x+2)-3(x+2)=0`
`<=> (x-3)(x+2)=0`
`<=>`\(\left[ \begin{array}{l}x-3=0\\x+2=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=3\\x=-2\end{array} \right.\)
Vậy `x in {3; -2}`
`f) x^2 = -4 -5x`
`<=> x^2 + 5x + 4=0`
`<=> x^2 +x + 4x+4=0`
`<=> x(x+1)+4(x+1)=0`
`<=> (x+4)(x+1)=0`
`<=>`\(\left[ \begin{array}{l}x+4=0\\x+1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-4\\x=-1\end{array} \right.\)
Vaayj `x in {-4; -1}`
