Question

3х^2-2х больше 0, помогите пожалуйста

Answer 1

$3x^{2} -2x\ \textgreater \ 0$
$x(3x-2)\ \textgreater \ 0$

Answer 2

Solving the Inequality 3x^2 - 2x > 0

To solve the inequality 3x^2 - 2x > 0, we can use the following steps:

1. Factorize the Inequality: Factorize the quadratic expression if possible. 2. Find the Critical Points: Find the critical points by setting the expression equal to zero and solving for x. 3. Test Intervals: Test the intervals defined by the critical points to determine where the inequality holds true.

Let's go through each step in detail.

Step 1: Factorize the Inequality

The given inequality is a quadratic expression. Factoring it will help us understand its behavior.

Step 2: Find the Critical Points

The critical points are the points where the expression equals zero. These points will help us determine the intervals where the inequality holds true.

Step 3: Test Intervals

We will test the intervals defined by the critical points to determine where the inequality holds true.

Let's proceed with the calculations.

Step 1: Factorize the Inequality

The given inequality is 3x^2 - 2x > 0. Factoring this quadratic expression, we get:

3x^2 - 2x > 0 x(3x - 2) > 0

Step 2: Find the Critical Points

To find the critical points, we set each factor equal to zero and solve for x:

1. x = 0 2. 3x - 2 = 0 3x = 2 x = 2/3

So, the critical points are x = 0 and x = 2/3.

Step 3: Test Intervals

We will test the intervals defined by the critical points to determine where the inequality holds true.

- Interval 1: x < 0 - Interval 2: 0 < x < 2/3 - Interval 3: x > 2/3

We will now determine in which intervals the inequality holds true.

Conclusion

After analyzing the critical points and testing the intervals, we find that the inequality 3x^2 - 2x > 0 holds true for the intervals x < 0 and x > 2/3.

This means that the solution to the inequality 3x^2 - 2x > 0 is x < 0 or x > 2/3.