What are the solutions to the equation 0=x^3-2x+1 ?

The solutions to the equation 0=x^3-2x+1 are x=1,x=(-1+sqrt(5))/2 ,x=(-1-sqrt(5))/2

Find the zeros of 0=x^3-2x+1

The zeros of 0=x^3-2x+1 are x=1,x=(-1+sqrt(5))/2 ,x=(-1-sqrt(5))/2

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

x = 1, x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

Decimal Notation

x = 1, x = 0.61803 \dots, x = - 1.61803 \dots

Solution steps

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

Switch sides

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x - 1 = 0 : x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

The solutions are

x = 1, x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

- x^{4} + x^{3} + 45 x^{2} - 25 x - 500 = 0

x = \frac{2}{3} π r^{3}, r

49 y^{3} - 16 y = 0

- 3 x^{3} - 8 x^{2} + 3 = 0

(x^{3} - 9) = 0

What are the solutions to the equation 0=x^3-2x+1 ?
The solutions to the equation 0=x^3-2x+1 are x=1,x=(-1+sqrt(5))/2 ,x=(-1-sqrt(5))/2
Find the zeros of 0=x^3-2x+1
The zeros of 0=x^3-2x+1 are x=1,x=(-1+sqrt(5))/2 ,x=(-1-sqrt(5))/2