a: \(8x^3-12x^2+6x-1=0\)
=>\(\left(2x-1\right)^3=0\)
=>2x-1=0
=>2x=1
=>\(x=\dfrac{1}{2}\)
b: \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-10\)
=>\(x^3+3x^2+3x+1-x^3+3x^2-3x+1-6\left(x^2-2x+1\right)=-10\)
=>\(6x^2+2-6x^2+12x-6=-10\)
=>12x-4=-10
=>12x=-6
=>\(x=-\dfrac{6}{12}=-\dfrac{1}{2}\)
c: \(\left(x-1\right)\left(x^2+x+1\right)+x\left(x+2\right)\left(2-x\right)=5\)
=>\(x^3-1+x\left(4-x^2\right)=5\)
=>\(x^3-1+4x-x^3=5\)
=>4x-1=5
=>4x=6
=>\(x=\dfrac{3}{2}\)
d: \(\left(2x-1\right)^3-8x^3=\left(1-3x\right)\left(4x+1\right)\)
=>\(8x^3-12x^2+6x-1-8x^3=4x+1-12x^2-3x\)
=>\(-12x^2+6x-1=-12x^2+x+1\)
=>6x-1=x+1
=>5x=2
=>\(x=\dfrac{2}{5}\)
