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

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

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

The zeros of (3x-1)^2=(3x-1)^3 are x= 1/3 ,x= 2/3

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

x = \frac{1}{3}, x = \frac{2}{3}

Decimal Notation

x = 0.33333 \dots, x = 0.66666 \dots

Solution steps

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

Expand

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

Expand

(3 x - 1)^{3} : 27 x^{3} - 27 x^{2} + 9 x - 1

9 x^{2} - 6 x + 1 = 27 x^{3} - 27 x^{2} + 9 x - 1

Switch sides

27 x^{3} - 27 x^{2} + 9 x - 1 = 9 x^{2} - 6 x + 1

Move

1

to the left side

27 x^{3} - 27 x^{2} + 9 x - 2 = 9 x^{2} - 6 x

Move

6 x

to the left side

27 x^{3} - 27 x^{2} + 15 x - 2 = 9 x^{2}

Move

9 x^{2}

to the left side

27 x^{3} - 36 x^{2} + 15 x - 2 = 0

Factor

27 x^{3} - 36 x^{2} + 15 x - 2 : (3 x - 1)^{2} (3 x - 2)

(3 x - 1)^{2} (3 x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x - 1 = 0 or 3 x - 2 = 0

Solve

3 x - 1 = 0 : x = \frac{1}{3}

Solve

3 x - 2 = 0 : x = \frac{2}{3}

The solutions are

x = \frac{1}{3}, x = \frac{2}{3}

50 \cdot x^{30} = 1000

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

3 x^{3} + x^{2} - 20 x + 12 = 0

4 (x^{6} + 5) = 2 x + 10

y, u = y^{3}

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