What are the solutions to the equation 81x^3=x^2 ?

The solutions to the equation 81x^3=x^2 are x=0,x= 1/81

Find the zeros of 81x^3=x^2

The zeros of 81x^3=x^2 are x=0,x= 1/81

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81 x^{3} = x^{2}

x = 0, x = \frac{1}{81}

Decimal Notation

x = 0, x = 0.01234 \dots

Solution steps

81 x^{3} = x^{2}

Move

x^{2}

to the left side

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

Factor

81 x^{3} - x^{2} : x^{2} (81 x - 1)

x^{2} (81 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 81 x - 1 = 0

Solve

81 x - 1 = 0 : x = \frac{1}{81}

The solutions are

x = 0, x = \frac{1}{81}

3 m^{3} + 12 m^{2} - 135 m = 0

x^{4} - 6 x^{2} + 20 x - 24 = 0

x^{2} (x - 3) = 16 (x - 3)

3 x^{3} + 1 = x^{2} + 3 x

x^{3} + 4 x^{2} - 5 x = - 3 x^{2} - 5 x + 15

What are the solutions to the equation 81x^3=x^2 ?
The solutions to the equation 81x^3=x^2 are x=0,x= 1/81
Find the zeros of 81x^3=x^2
The zeros of 81x^3=x^2 are x=0,x= 1/81