Đáp án:
`a)` `S={5;1;-1}`
`b)` `S={1;2}`
Giải thích các bước giải:
`a)`
`x^3-5x^2-x+5=0`
`<=>x^2(x-5)-(x-5)=0`
`<=>(x-5)(x^2-1)=0`
`<=>(x-5)(x-1)(x+1)=0`
`<=>[(x-5=0),(x-1=0),(x+1=0):}`
`<=>[(x=5),(x=1),(x=-1):}`
Vậy `S={5;1;-1}`
`b)` `x^2(x-1)=4x^2-8x+4`
`<=>x^2(x-1)=4(x^2-2x+1)`
`<=>x^2(x-1)=4(x-1)^2`
`<=>x^2(x-1)-4(x-1)^2=0`
`<=>(x-1)[x^2-4(x-1)]=0`
`<=>(x-1)(x^2-4x+4)=0`
`<=>(x-1)(x-2)^2=0`
`<=>[(x-1=0),((x-2)^2=0):}`
`<=>[(x=1),(x-2=0):}`
`<=>[(x=1),(x=2):}`
Vậy `S={1;2}`.
