Đáp án:`a)S={(\root{3}{4}+1)/2}.`
`b)S={(-1)/(1+\root{3}{-2})}.`
Giải thích các bước giải:
`1)8x^3-12x^2+6x-5=0`
`<=>(2x)^3-3.(2x)^{2}.1+3.2x.1-1-4=0`
`<=>(2x-1)^3-4=0`
`<=>(2x-1)^3=4`
`<=>2x-1=\root{3}{4}`
`<=>2x=\root{3}{4}+1`
`<=>x=(\root{3}{4}+1)/2`
Vậy `S={(\root{3}{4}+1)/2}.`
`2)3x^3+3x^2+3x=-1`
`<=>3x^3+3x^2+3x+1=0`
`<=>x^3+3x^2+3x+1+2x^3=0`
`<=>(x+1)^3+2x^3=0`
`<=>(x+1)^3=-2x^3`
`<=>x+1=\root{3}{-2}x`
`<=>x(1+\root{3}{-2})=-1`
`<=>x=(-1)/(1+\root{3}{-2})`
Vậy `S={(-1)/(1+\root{3}{-2})}.`
