`a)` `(x-1)^3 + (x-2)^3 + ( 2 - 2x)^3 = 0`

`=> (x-1)^3 + (x-2)^3 + [2(1-x)]^3 = 0`

`=> (x-1)^3 + (x-2)^3 -8(x-1)^3 = 0`

`=> (x-2)^3 - 7(x-1)^3 = 0`

`=> (x-2)^3 = 7(x-1)^3`

`=> x-2 = \root{3}{7}(x-1)`

`=> x - 2 =  \root{3}{7} x -  \root{3}{7}`

`=> x -  \root{3}{7} x = 2 -  \root{3}{7}`

`=> x ( 1 -  \root{3}{7} ) = 2 -  \root{3}{7} `

`=> x = (2 - \root{3}{7} )/(1 -  \root{3}{7} )`