Question

6х-x^2 >0 Укажите решение неравенства

Answer 1

Ответ:

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Объяснение:

Answer 2

Solution to the Inequality 6x - x^2 > 0

To find the solution to the inequality 6x - x^2 > 0, we need to determine the values of x that satisfy the inequality. Let's break down the steps to find the solution:

1. Factor the quadratic equation: To solve the inequality, we first need to factor the quadratic equation 6x - x^2 > 0. The factored form of the equation is (x - 2)(x - 3) < 0.

2. Determine the critical points: The critical points are the values of x that make the inequality equal to zero. In this case, the critical points are x = 2 and x = 3.

3. Create a sign chart: To determine the solution, we create a sign chart by dividing the number line into intervals based on the critical points.

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

4. Test the intervals: We choose a test point from each interval and substitute it into the inequality to determine the sign of the expression.

- For Interval 1 (x < 2), we can choose x = 0. Substituting x = 0 into the inequality, we get (0 - 2)(0 - 3) < 0, which simplifies to 6 < 0. Since this is false, Interval 1 is not part of the solution.

- For Interval 2 (2 < x < 3), we can choose x = 2.5. Substituting x = 2.5 into the inequality, we get (2.5 - 2)(2.5 - 3) < 0, which simplifies to -0.5 < 0. Since this is true, Interval 2 is part of the solution.

- For Interval 3 (x > 3), we can choose x = 4. Substituting x = 4 into the inequality, we get (4 - 2)(4 - 3) < 0, which simplifies to 2 < 0. Since this is false, Interval 3 is not part of the solution.

5. Determine the solution: Based on the sign chart and the test intervals, the solution to the inequality 6x - x^2 > 0 is 2 < x < 3.

Please note that the solution is exclusive, meaning that x cannot be equal to 2 or 3.

Conclusion

The solution to the inequality 6x - x^2 > 0 is 2 < x < 3.