`***`Lời giải`***`
a)
`x^2-9x=0`
`<=>x(x-9)=0`
`+)x=0`
`+)x-9=0<=>x=9`
Vậy `S={0;9}`
b)
`4x(x+1)=8(x+1)`
`<=>4x^2+4x=8x+8`
`<=>4x^2+4x-8x-8=0`
`<=>4x^2-4x-8=0`
`<=>4(x^2-x-2)=0`
`<=>x^2+x-2x-2=0`
`<=>(x^2+x)+(-2x-2)=0`
`<=>x(x+1)-2(x+1)=0`
`<=>(x-2)(x+1)=0`
`+)x-2=0<=>x=2`
`+)x+1=0<=>x=-1`
Vậy `S={2;-1}`
c)
`x(2x-6)-2(6-2x)=0`
`<=>2x(x-3)+4(x-3)=0`
`<=>(2x+4)(x-3)=0`
`<=>2(x+2)(x-3)=0`
`<=>(x+2)(x-3)=0`
`+)x+2=0<=>x=-2`
`+)x-3=0<=>x=3`
Vậy `S={-2;3}`
d)
`2-x=2(x-2)^3`
`<=>2-x-2(x-2)^3=0`
`<=>-(x-2)-2(x-2)^3=0`
`<=>(x-2)[-1-2(x-2)^2]=0`
`<=>(x-2)[-1-2(x^2-4x+4)]=0`
`<=>(x-2)(-1-2x^2+8x-8)=0`
`<=>(x-2)(-2x^2+8x-9)=0`
`<=>(x-2)(2x^2-8x+9)=0`
Mà `2x^2-8x+9`
`=2x^2-8x+8+1`
`=2(x^2-4x+4)+1`
`=2(x-2)^2+1`
Với `∀x` Ta có: `(x-2)^2≥0<=>2(x-2)^2+1≥1>0`
`=>x-2=0`
`<=>x=2`
Vậy `S={2}`
e)
`81(x-2)^4-3(x-2)=0`
`<=>[3(x-2)]^4-3(x-2)=0`
`<=>3(x-2){[3(x-2)]^3-1}=0`
`<=>3(x-2)(3x-7)(9x^2-33x+31)=0`
`<=>(x-2)(3x-7)(9x^2-33x+31)=0`
Mà `9x^2-33x+31`
`=9x^2-33x+121/4+3/4`
`=(3x-11/2)^2+3/4`
Với `∀x` Ta có:`(3x-11/2)^2≥0<=>(3x-11/2)^2+3/4≥3/4>0`
`=>(x-2)(3x-7)=0`
`+)x-2=0<=>x=2`
`+)3x-7=0<=>x=7/3`
Vậy `S={2;7/3}`
f)
`(x+1)^5=16(x+1)`
`<=>(x+1)^5-16(x+1)=0`
`<=>(x+1)[(x+1)^4-16]=0`
`<=>(x+1)[(x+1)^4-2^4]=0`
`<=>(x+1)[(x+1)^2-2^2][(x+1)^2+2^2]=0`
`<=>(x+1)(x+1-2)(x+1+2)(x^2+2x+5)=0`
`<=>(x+1)(x-1)(x+3)(x^2+2x+5)=0`
Mà`x^2+2x+5`
`=x^2+2x+1+4`
`=(x+1)^2+4`
Với `∀x` Ta có: `(x+1)^2≥0<=>(x+1)^2+4≥4>0`
`=>(x+1)(x-1)(x+3)=0`
`+)x+1=0<=>x=-1`
`+)x-1=0<=>x=1`
`+)x+3=0<=>x=-3`
Vậy `S={-1;1;-3}`