What are the solutions to the equation x^3-9x^2+27x-27=64 ?

The solutions to the equation x^3-9x^2+27x-27=64 are x=7,x=1+2sqrt(3)i,x=1-2sqrt(3)i

Find the zeros of x^3-9x^2+27x-27=64

The zeros of x^3-9x^2+27x-27=64 are x=7,x=1+2sqrt(3)i,x=1-2sqrt(3)i

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x^{3} - 9 x^{2} + 27 x - 27 = 64

x = 7, x = 1 + 23 i, x = 1 - 23 i

Solution steps

x^{3} - 9 x^{2} + 27 x - 27 = 64

Move

64

to the left side

x^{3} - 9 x^{2} + 27 x - 91 = 0

Factor

x^{3} - 9 x^{2} + 27 x - 91 : (x - 7) (x^{2} - 2 x + 13)

(x - 7) (x^{2} - 2 x + 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 7 = 0 or x^{2} - 2 x + 13 = 0

Solve

x - 7 = 0 : x = 7

Solve

x^{2} - 2 x + 13 = 0 : x = 1 + 23 i, x = 1 - 23 i

The solutions are

x = 7, x = 1 + 23 i, x = 1 - 23 i

x^{4} + 8 x^{2} + 7 = 0

x^{4} + 2 x^{2} + 3 = 0

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

- y^{4} + 4 y^{3} + 12 y^{2} = 0

1 (1 + x)^{12} = 2

What are the solutions to the equation x^3-9x^2+27x-27=64 ?
The solutions to the equation x^3-9x^2+27x-27=64 are x=7,x=1+2sqrt(3)i,x=1-2sqrt(3)i
Find the zeros of x^3-9x^2+27x-27=64
The zeros of x^3-9x^2+27x-27=64 are x=7,x=1+2sqrt(3)i,x=1-2sqrt(3)i