What are the solutions to the equation 2(2^2)-6y+y^3=-1 ?

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

Find the zeros of 2(2^2)-6y+y^3=-1

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

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2 (2^{2}) - 6 y + y^{3} = - 1

y = - 3, y = \frac{3}{2} + i \frac{3}{2}, y = \frac{3}{2} - i \frac{3}{2}

Solution steps

2 (2^{2}) - 6 y + y^{3} = - 1

Expand

2 (2^{2}) - 6 y + y^{3} : 8 - 6 y + y^{3}

8 - 6 y + y^{3} = - 1

Move

1

to the left side

y^{3} - 6 y + 9 = 0

Factor

y^{3} - 6 y + 9 : (y + 3) (y^{2} - 3 y + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

y + 3 = 0 : y = - 3

Solve

y^{2} - 3 y + 3 = 0 : y = \frac{3}{2} + i \frac{3}{2}, y = \frac{3}{2} - i \frac{3}{2}

The solutions are

y = - 3, y = \frac{3}{2} + i \frac{3}{2}, y = \frac{3}{2} - i \frac{3}{2}

531827 = 435894 \cdot (1 + x)^{8}

x^{2} + 21 x - x^{5} = 0

1000 = x^{3}

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

x^{7} + 7 x^{4} - 8 x = 0

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