What are the solutions to the equation (1/3 x)^2=(1/6 x)^3 ?

The solutions to the equation (1/3 x)^2=(1/6 x)^3 are x=0,x=24

Find the zeros of (1/3 x)^2=(1/6 x)^3

The zeros of (1/3 x)^2=(1/6 x)^3 are x=0,x=24

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(\frac{1}{3} x)^{2} = (\frac{1}{6} x)^{3}

x = 0, x = 24

Solution steps

(\frac{1}{3} x)^{2} = (\frac{1}{6} x)^{3}

Expand

(\frac{1}{3} x)^{2} : \frac{1}{9} x^{2}

Expand

(\frac{1}{6} x)^{3} : \frac{1}{216} x^{3}

\frac{1}{9} x^{2} = \frac{1}{216} x^{3}

Switch sides

\frac{1}{216} x^{3} = \frac{1}{9} x^{2}

Move

\frac{1}{9} x^{2}

to the left side

\frac{1}{216} x^{3} - \frac{1}{9} x^{2} = 0

Factor

\frac{1}{216} x^{3} - \frac{1}{9} x^{2} : x^{2} (\frac{x}{216} - \frac{1}{9})

x^{2} (\frac{x}{216} - \frac{1}{9}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or \frac{x}{216} - \frac{1}{9} = 0

Solve

\frac{x}{216} - \frac{1}{9} = 0 : x = 24

The solutions are

x = 0, x = 24

z^{3} - z + 6 = 0

2 x^{3} - 3 x^{2} - 10 x + 15 = 0

x = - x^{3}

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

x^{3} + 2 x^{2} - 40 x + 64 = 0

What are the solutions to the equation (1/3 x)^2=(1/6 x)^3 ?
The solutions to the equation (1/3 x)^2=(1/6 x)^3 are x=0,x=24
Find the zeros of (1/3 x)^2=(1/6 x)^3
The zeros of (1/3 x)^2=(1/6 x)^3 are x=0,x=24