What are the solutions to the equation 3x-1=(x-1)^3 ?

The solutions to the equation 3x-1=(x-1)^3 are x=0,x=3

Find the zeros of 3x-1=(x-1)^3

The zeros of 3x-1=(x-1)^3 are x=0,x=3

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3 x - 1 = (x - 1)^{3}

x = 0, x = 3

Solution steps

3 x - 1 = (x - 1)^{3}

Expand

(x - 1)^{3} : x^{3} - 3 x^{2} + 3 x - 1

3 x - 1 = x^{3} - 3 x^{2} + 3 x - 1

Switch sides

x^{3} - 3 x^{2} + 3 x - 1 = 3 x - 1

Move

1

to the right side

x^{3} - 3 x^{2} + 3 x = 3 x

Move

3 x

to the left side

x^{3} - 3 x^{2} = 0

Factor

x^{3} - 3 x^{2} : x^{2} (x - 3)

x^{2} (x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 3 = 0

Solve

x - 3 = 0 : x = 3

The solutions are

x = 0, x = 3

2 x^{4} - 4 x^{3} - 2 x + 1 = 0

0.1 x^{4} - 1355 x^{2} + 2740000 = 0

- 3 x^{3} - 5 x^{2} - 2 x = 0

3 x^{3} + 9 x^{2} - 7 x + 4 = 0

3 x^{1} - 4 x^{2} - 7 x^{3} = - 2

What are the solutions to the equation 3x-1=(x-1)^3 ?
The solutions to the equation 3x-1=(x-1)^3 are x=0,x=3
Find the zeros of 3x-1=(x-1)^3
The zeros of 3x-1=(x-1)^3 are x=0,x=3