Question

24х - 6х в третьей степени = 0

Answer 1

$24x-6x^3=0$
$6x*(4-x^2)=0$
$x*(4-x^2)=0$
$x=0$
$4-x^2=0$
$x_{1} =0$
$x_{2}=2$
$x_{3}=-2$

Answer 2

To solve the equation 24x - 6x^3 = 0, we need to find the values of x that satisfy the equation. To do that, we can factor out the common term "6x" from both terms:

6x(4 - x^2) = 0

Now, we have a product of two factors that are equal to zero. According to the zero-product property, if the product of two factors is zero, then at least one of the factors must be zero.

So, we can set each factor equal to zero and solve for x:

1. 6x = 0 Divide both sides by 6: x = 0

2. 4 - x^2 = 0 Add x^2 to both sides: 4 = x^2

   Now, take the square root of both sides: √(4) = √(x^2) 2 = |x|

   Since we have the absolute value of x (|x|), there are two possible solutions for x: a. x = 2 b. x = -2

So, the three solutions to the equation 24x - 6x^3 = 0 are x = 0, x = 2, and x = -2.