What are the solutions to the equation u^3+8=(u+2) ?

The solutions to the equation u^3+8=(u+2) are u=-2,u=1+sqrt(2)i,u=1-sqrt(2)i

Find the zeros of u^3+8=(u+2)

The zeros of u^3+8=(u+2) are u=-2,u=1+sqrt(2)i,u=1-sqrt(2)i

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u^{3} + 8 = (u + 2)

u = - 2, u = 1 + 2 i, u = 1 - 2 i

Solution steps

u^{3} + 8 = (u + 2)

Refine

u^{3} + 8 = u + 2

Move

2

to the left side

u^{3} + 6 = u

Move

u

to the left side

u^{3} + 6 - u = 0

Write in the standard form

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

u^{3} - u + 6 = 0

Factor

u^{3} - u + 6 : (u + 2) (u^{2} - 2 u + 3)

(u + 2) (u^{2} - 2 u + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

u + 2 = 0 or u^{2} - 2 u + 3 = 0

Solve

u + 2 = 0 : u = - 2

Solve

u^{2} - 2 u + 3 = 0 : u = 1 + 2 i, u = 1 - 2 i

The solutions are

u = - 2, u = 1 + 2 i, u = 1 - 2 i

- 6 + w^{3} = - 9

54 = (6 - p^{4}) 3

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

(x^{2} - 8)^{2} - 2 (x^{2} - 8) = - 1

- 2 x^{4} - x^{3} + 14 x^{2} + 19 x + 6 = 0

What are the solutions to the equation u^3+8=(u+2) ?
The solutions to the equation u^3+8=(u+2) are u=-2,u=1+sqrt(2)i,u=1-sqrt(2)i
Find the zeros of u^3+8=(u+2)
The zeros of u^3+8=(u+2) are u=-2,u=1+sqrt(2)i,u=1-sqrt(2)i