Solve the following equation. $$ 3 x^{3}=12 x $$

Question

UpStudy AI · Accepted Answer

1. Start with the equation:
   
   $$
   3x^3 = 12x
   $$

2. Subtract $$12x$$ from both sides to set the equation to zero:

$$
   3x^3 - 12x = 0
   $$

3. Factor out the common factor $$3x$$:

$$
   3x(x^2 - 4) = 0
   $$

4. Factor the quadratic $$x^2 - 4$$ as a difference of squares:

$$
   x^2 - 4 = (x-2)(x+2)
   $$

5. Thus, the factored equation is:

$$
   3x(x-2)(x+2) = 0
   $$

6. Set each factor equal to zero and solve:

- From $$3x = 0$$: 
     
     $$
     x = 0
     $$
     
   - From $$x-2 = 0$$: 
     
     $$
     x = 2
     $$
     
   - From $$x+2 = 0$$: 
     
     $$
     x = -2
     $$

7. The solutions of the equation are:

$$
   x = -2, \quad x = 0, \quad x = 2
   $$
The solutions are $$ x = -2 $$, $$ x = 0 $$, and $$ x = 2 $$.

Solve the following equation.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions