What are the solutions to the equation 16a^3(3x^2-4a^2)=0 ?

The solutions to the equation 16a^3(3x^2-4a^2)=0 are x=(2a)/(sqrt(3)),x=-(2a)/(sqrt(3))

Find the zeros of 16a^3(3x^2-4a^2)=0

The zeros of 16a^3(3x^2-4a^2)=0 are x=(2a)/(sqrt(3)),x=-(2a)/(sqrt(3))

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16 a^{3} (3 x^{2} - 4 a^{2}) = 0

x = \frac{2 a}{3}, x = - \frac{2 a}{3}

Solution steps

16 a^{3} (3 x^{2} - 4 a^{2}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x^{2} - 4 a^{2} = 0

Move

4 a^{2}

to the right side

3 x^{2} = 4 a^{2}

Divide both sides by

3

x^{2} = \frac{4 a ^{2}}{3}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = \frac{4 a ^{2}}{3}, x = - \frac{4 a ^{2}}{3}

Simplify

\frac{4 a ^{2}}{3} : \frac{2 a}{3}

Simplify

- \frac{4 a ^{2}}{3} : - \frac{2 a}{3}

x = \frac{2 a}{3}, x = - \frac{2 a}{3}

3 (x + 2)^{2} - 4 = 11

x (2 x - 4) - 100 = 4 (6 - x) - 17

2 x^{2} - 3 x - 42 = 2

9 x^{2} - 25 x + 16 = 0

n^{2} - 10 = 3 n

What are the solutions to the equation 16a^3(3x^2-4a^2)=0 ?
The solutions to the equation 16a^3(3x^2-4a^2)=0 are x=(2a)/(sqrt(3)),x=-(2a)/(sqrt(3))
Find the zeros of 16a^3(3x^2-4a^2)=0
The zeros of 16a^3(3x^2-4a^2)=0 are x=(2a)/(sqrt(3)),x=-(2a)/(sqrt(3))