What are the solutions to the equation x^3-4x-2=1 ?

The solutions to the equation x^3-4x-2=1 are x=-1,x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2

Find the zeros of x^3-4x-2=1

The zeros of x^3-4x-2=1 are x=-1,x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2

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

x = - 1, x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

Decimal Notation

x = - 1, x = 2.30277 \dots, x = - 1.30277 \dots

Solution steps

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

Move

1

to the left side

x^{3} - 4 x - 3 = 0

Factor

x^{3} - 4 x - 3 : (x + 1) (x^{2} - x - 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

x^{2} - x - 3 = 0 : x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

The solutions are

x = - 1, x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

x^{3} - 1 = 1

(x^{2} - 5)^{2} - 3 (x^{2} - 5) = 4

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

m^{3} = \frac{8}{27}

3 x^{4} - 3 x = 0

What are the solutions to the equation x^3-4x-2=1 ?
The solutions to the equation x^3-4x-2=1 are x=-1,x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2
Find the zeros of x^3-4x-2=1
The zeros of x^3-4x-2=1 are x=-1,x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2