What are the solutions to the equation (x-2)^3=3x-6 ?

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

Find the zeros of (x-2)^3=3x-6

The zeros of (x-2)^3=3x-6 are x=2,x=2+sqrt(3),x=2-sqrt(3)

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(x - 2)^{3} = 3 x - 6

x = 2, x = 2 + 3, x = 2 - 3

Decimal Notation

x = 2, x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

(x - 2)^{3} = 3 x - 6

Expand

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

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

Move

6

to the left side

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

Move

3 x

to the left side

x^{3} - 6 x^{2} + 9 x - 2 = 0

Factor

x^{3} - 6 x^{2} + 9 x - 2 : (x - 2) (x^{2} - 4 x + 1)

(x - 2) (x^{2} - 4 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} - 4 x + 1 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 4 x + 1 = 0 : x = 2 + 3, x = 2 - 3

The solutions are

x = 2, x = 2 + 3, x = 2 - 3

x^{4} - 8 x^{2} = 9

x^{4} - 5 x^{2} + 4 x = 0

(x + 2) (x - 5) (3 x - 4) = 0

2 x^{3} + 4 x^{2} - 16 x = 0

x, x^{4} + y^{4} = 16

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