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

The solutions to the equation (x-2)^3=-1 are x=1,x= 5/2+i(sqrt(3))/2 ,x= 5/2-i(sqrt(3))/2

Find the zeros of (x-2)^3=-1

The zeros of (x-2)^3=-1 are x=1,x= 5/2+i(sqrt(3))/2 ,x= 5/2-i(sqrt(3))/2

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

x = 1, x = \frac{5}{2} + i \frac{3}{2}, x = \frac{5}{2} - i \frac{3}{2}

Solution steps

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

Expand

(x - 2)^{3} : x^{3} - 6 x^{2} + 12 x - 8

x^{3} - 6 x^{2} + 12 x - 8 = - 1

Move

1

to the left side

x^{3} - 6 x^{2} + 12 x - 7 = 0

Factor

x^{3} - 6 x^{2} + 12 x - 7 : (x - 1) (x^{2} - 5 x + 7)

(x - 1) (x^{2} - 5 x + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} - 5 x + 7 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 5 x + 7 = 0 : x = \frac{5}{2} + i \frac{3}{2}, x = \frac{5}{2} - i \frac{3}{2}

The solutions are

x = 1, x = \frac{5}{2} + i \frac{3}{2}, x = \frac{5}{2} - i \frac{3}{2}

f^{3} = \frac{3}{2} - \frac{3}{3}

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

x^{3} = - 21

x^{3} - 8 x^{2} + 9 x = 72

z^{4} + z^{2} - i 3 = 0

What are the solutions to the equation (x-2)^3=-1 ?
The solutions to the equation (x-2)^3=-1 are x=1,x= 5/2+i(sqrt(3))/2 ,x= 5/2-i(sqrt(3))/2
Find the zeros of (x-2)^3=-1
The zeros of (x-2)^3=-1 are x=1,x= 5/2+i(sqrt(3))/2 ,x= 5/2-i(sqrt(3))/2