(2x-1)³+8=0
[(2x-1)+2][(2x-1)²-2(2x-1)+4]=0
(2x-3)(4x²-4x+1-4x+2+4)=0
(2x-3)(4x²-8x+7)=0
∵4x²-8x+7
=4(x²-2x+1)+3
=4(x-1)²+3
≥3
∴2x-3=0
∴x=3/2
(2x-1)³+8=0
[(2x-1)+2][(2x-1)²-2(2x-1)+4]=0
(2x-3)(4x²-4x+1-4x+2+4)=0
(2x-3)(4x²-8x+7)=0
∵4x²-8x+7
=4(x²-2x+1)+3
=4(x-1)²+3
≥3
∴2x-3=0
∴x=3/2