Question

Answer 1

Bài 5:

a: \(4x^3+108=0\)

=>\(4x^3=-108\)

=>\(x^3=-27\)

=>x=-3

b: \(1000x^3-8=0\)

=>\(1000x^3=8\)

=>\(x^3=\frac{8}{1000}=\frac{1}{125}=\left(\frac15\right)^3\)

=>\(x=\frac15\)

c: \(\left(x+3\right)^3-64=0\)

=>\(\left(x+3\right)^3=64=4^3\)

=>x+3=4

=>x=1

d: \(\left(2x-1\right)^3+125=0\)

=>\(\left(2x-1\right)^3=-125=\left(-5\right)^3\)

=>2x-1=-5

=>2x=-4

=>x=-2

e: \(\left(\frac13-2x\right)^3+\frac{27}{8}=0\)

=>\(\left(\frac13-2x\right)^3=-\frac{27}{8}=\left(-\frac32\right)^3\)

=>\(-2x+\frac13=-\frac32\)

=>\(-2x=-\frac32-\frac13=\frac{-9-2}{6}=-\frac{11}{6}\)

=>\(x=\frac{11}{12}\)

f: \(\left(2x-1\right)^3-\left(x+3\right)^3=0\)

=>\(\left(2x-1\right)^3=\left(x+3\right)^3\)

=>2x-1=x+3

=>x=4

Bài 3:

a: \(\left(x+2\right)^3+\left(x-2\right)^3-2x\left(x^2+12\right)\)

\(=x^3+6x^2+12x+8+x^3-6x^2+12x-8-2x^3-24x\)

=0

b: \(\left(x-1\right)^3-\left(x+1\right)^3+6\left(x+1\right)\left(x-1\right)\)

\(=x^3-3x^2+3x-1-x^3-3x^2-3x-1+6\left(x^2-1\right)\)

\(=-6x^2-2+6x^2-6=-2-6=-8\)

c: \(\left(x-1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(1-x\right)\)

\(=x^3-3x^2+3x-1-x^3+1-3x+3x^2\)

=0

d: \(\left(2x+\frac13\right)\left(4x^2-\frac23x+\frac19\right)-\left(8x^3-\frac{1}{27}\right)\)

\(=8x^3+\frac{1}{27}-8x^3+\frac{1}{27}=\frac{2}{27}\)