What are the solutions to the equation b^3-b=6 ?

The solutions to the equation b^3-b=6 are b=2,b=-1+sqrt(2)i,b=-1-sqrt(2)i

Find the zeros of b^3-b=6

The zeros of b^3-b=6 are b=2,b=-1+sqrt(2)i,b=-1-sqrt(2)i

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b^{3} - b = 6

b = 2, b = - 1 + 2 i, b = - 1 - 2 i

Solution steps

b^{3} - b = 6

Move

6

to the left side

b^{3} - b - 6 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

b - 2 = 0 : b = 2

Solve

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

The solutions are

b = 2, b = - 1 + 2 i, b = - 1 - 2 i

7 x - x^{3} = 0

4 x^{3} + 15 x^{2} + 8 x - 4 = 0

x^{3} - 15 x - 126 = 0

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

9 x^{3} = 4 x^{2}

What are the solutions to the equation b^3-b=6 ?
The solutions to the equation b^3-b=6 are b=2,b=-1+sqrt(2)i,b=-1-sqrt(2)i
Find the zeros of b^3-b=6
The zeros of b^3-b=6 are b=2,b=-1+sqrt(2)i,b=-1-sqrt(2)i