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

The solutions to the equation x+x^3=2 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

Find the zeros of x+x^3=2

The zeros of x+x^3=2 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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x + x^{3} = 2

x = 1, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

Solution steps

x + x^{3} = 2

Move

2

to the left side

x + x^{3} - 2 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} + x - 2 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x + 2 = 0 : x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

The solutions are

x = 1, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

x, x^{3} - 49 x = 0

(1 - x) (1 - x) (- 1 - x) - i (- i) (- 1 - x) = 0

36 x^{4} - 25 x^{2} + 4 = 0

165 = 5 x^{3}

2 = 6 x^{5}

What are the solutions to the equation x+x^3=2 ?
The solutions to the equation x+x^3=2 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2
Find the zeros of x+x^3=2
The zeros of x+x^3=2 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2