What are the solutions to the equation x^3-3x^2+3x-1=1 ?

The solutions to the equation x^3-3x^2+3x-1=1 are x=2,x= 1/2+i(sqrt(3))/2 ,x= 1/2-i(sqrt(3))/2

Find the zeros of x^3-3x^2+3x-1=1

The zeros of x^3-3x^2+3x-1=1 are x=2,x= 1/2+i(sqrt(3))/2 ,x= 1/2-i(sqrt(3))/2

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

x = 2, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

Solution steps

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

Move

1

to the left side

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

Factor

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

(x - 2) (x^{2} - x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} - x + 1 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - x + 1 = 0 : x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

The solutions are

x = 2, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

2 x^{4} - 21 x^{2} + 45 = 0

2 x^{3} = x^{2}

4 x^{3} + x^{2} - 36 x - 9 = 0

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

m^{3} = 2

What are the solutions to the equation x^3-3x^2+3x-1=1 ?
The solutions to the equation x^3-3x^2+3x-1=1 are x=2,x= 1/2+i(sqrt(3))/2 ,x= 1/2-i(sqrt(3))/2
Find the zeros of x^3-3x^2+3x-1=1
The zeros of x^3-3x^2+3x-1=1 are x=2,x= 1/2+i(sqrt(3))/2 ,x= 1/2-i(sqrt(3))/2