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

The solutions to the equation x^3+2x-1=2 are x=1,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2

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

The zeros of x^3+2x-1=2 are x=1,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2

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

x = 1, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

Solution steps

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

Move

2

to the left side

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

Factor

x^{3} + 2 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}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

The solutions are

x = 1, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

t^{3} = 8

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

x^{3} - 3 x^{2} = (x - 3) (x + 20)

t^{3} = t

x^{3} - 7 x - 4 = 0

What are the solutions to the equation x^3+2x-1=2 ?
The solutions to the equation x^3+2x-1=2 are x=1,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2
Find the zeros of x^3+2x-1=2
The zeros of x^3+2x-1=2 are x=1,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2