1)
`3x^2-3x(x-2)=36`
`<=>3x^2-3x^2+6x=36`
`<=>6x=36`
`<=>x=6`
vậy `S={6}`
2)
`x^2-2x+1=2`
`<=>(x-1)^2=2`
`<=>x-1=±sqrt2`
`<=>x=1±sqrt2`
vậy `S={1±sqrt2}`
3)
`x^2+7x=8`
`<=>x^2+7x-8=0`
`<=>x^2-x+8x-8=0`
`<=>x(x-1)+8(x-1)=0`
`<=>(x-1)(x+8)=0`
`<=>` \(\left[ \begin{array}{l}x-1=0\\x+8=0\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=1\\x=-8\end{array} \right.\)
vậy `S={1;-8}`
4)
`5x(x-1)=x-1`
`<=>5x^2-5x-x+1=0`
`<=>x(5x-1)-1(5x-1)=0`
`<=>(x-1)(5x-1)=0`
`<=>` \(\left[ \begin{array}{l}x-1=0\\5x-1=0\end{array} \right.\) `<=>`\(\left[ \begin{array}{l}x=1\\5x=1\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=1\\x=\frac{1}{5}\end{array} \right.\)
vậy `S={1;1/5}`
5)
`2(x+5)-x^2-5x=0`
`<=>2(x+5)-x(x+5)=0`
`<=>(2-x)(x+5)=0`
`<=>` \(\left[ \begin{array}{l}2-x=0\\x+5=0\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=2\\x=-5\end{array} \right.\)
vậy `S={2;-5}`
6)
`(2x-1)^2-4(x+7)(x-7)=0`
`<=>4x^2-4x+1-4(x^2-7^2)=0`
`<=>4x^2-4x+1-4x^2+196=0`
`<=>-4x+197=0`
`<=>-4x=-197`
`<=>x=49,25`
vậy `S={49,25}`
7)
`x^3-9x^3=27-27x`
`<=>x^3-9x^2-27+27x=0`
`<=>(x-3)^3=0`
`<=>x-3=0`
`<=>x=3`
vậy `S={3}`
8)
`-x^2-2x+15=0`
`<=>-x^2-5x+3x+15=0`
`<=>-x(x+5)+3(x+5)=0`
`<=>(3-x)(x+5)=0`
`<=>`\(\left[ \begin{array}{l}3-x=0\\x+5=0\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}x=3\\x=-5\end{array} \right.\)
vậy `S={3;-5}`
9)
`2x^2-5x+2=0`
`<=>2x^2-4x-x+2=0`
`<=>2x(x-2)-1(x-2)=0`
`<=>(2x-1)(x-2)=0`
`<=>` \(\left[ \begin{array}{l}2x-1=0\\x-2=0\end{array} \right.\) `<=>`\(\left[ \begin{array}{l}2x=1\\x=2\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=\frac{1}{2}\\x=2\end{array} \right.\)
vậy `S={1/2;2}`
10)
`9(3x-2)=-x^2(2-3x)`
`<=>9(3x-2)+x^2(2+3x)=0`
`<=>9(3x-2)-x^2(3x-2)=0`
`<=>(9-x^2)(3x-2)=0`
`<=>(3-x)(3+x)(3x-2)=0`
`<=>3-x=0;3+x=0;3x-2=0`
`<=>x=3;x=-3;3x=2`
`<=>x=3;x=-3;x=2/3`
vậy `S={3;-3;2/3}`