`a)`
`(x+1)(x+2)-x^2=17`
`<=>x^2+2x+x+2-x^2-17=0`
`<=>3x-15=0`
`<=>3x=15`
`<=>x=5`
Vậy `S={5}`
`b)`
`(x+1)^3+3x(2-x)-9(x-1)=18`
`<=>x^3+3x^2+3x+1+6x-3x^2-9x+9-18=0`
`<=>x^3-8=0`
`<=>x^3=8`
`<=>x=2`
Vậy `S={2}`
`c)`
`x^2(x-5)-9x+45=0`
`<=>x^2(x-5)-9(x-5)=0`
`<=>(x-5)(x^2-9)=0`
`<=>(x-5)(x-3)(x+3)=0`
`<=>`\(\left[ \begin{array}{l}x-5=0\\x-3=0\\x+3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=5\\x=3\\x=-3\end{array} \right.\)
Vậy `S={5;3;-3}`