Question

5x-x^2>0 Ребятаа, помогайте, погибаю как швед под Полтавой

Answer 1

5х - х² >0

5х - х² = 0

х(5 - х) = 0

х1 = 0  или    х2 = 5

                    ///////////////////
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                  0                 5

 ОТВЕТ   (0;5)

Answer 2

Solving the Inequality 5x - x^2 > 0

To solve the inequality 5x - x^2 > 0, we can use algebraic methods to find the values of x that satisfy the inequality.

Step 1: Finding the Critical Points

The first step is to find the critical points of the inequality, which are the points where the expression 5x - x^2 equals 0. We can do this by factoring the expression and setting each factor equal to 0.

Factoring the expression 5x - x^2, we get: 5x - x^2 = x(5 - x)

Setting each factor equal to 0 gives us the critical points: x = 0 and x = 5

Step 2: Testing Intervals

Next, we can test the intervals created by the critical points to determine when the inequality 5x - x^2 > 0 is satisfied.

- Interval 1: x < 0 - Interval 2: 0 < x < 5 - Interval 3: x > 5

Step 3: Determining the Solution

We can now test a value from each interval in the original inequality to see when it is satisfied.

- For x < 0, let's test x = -1: 5(-1) - (-1)^2 = -5 - 1 = -6 Since -6 is less than 0, the inequality is not satisfied for x < 0.

- For 0 < x < 5, let's test x = 1: 5(1) - (1)^2 = 5 - 1 = 4 Since 4 is greater than 0, the inequality is satisfied for 0 < x < 5.

- For x > 5, let's test x = 6: 5(6) - (6)^2 = 30 - 36 = -6 Since -6 is less than 0, the inequality is not satisfied for x > 5.

Conclusion: The solution to the inequality 5x - x^2 > 0 is: 0 < x < 5.

This means that the inequality is satisfied when x is between 0 and 5, exclusive.