Question

КАК РЕШИТЬ ПРИМЕР Х2+36Х<0

Answer 1

X^2+36x<0x
x(x+36)=0
x=0
x=-36
(0,-36)

Answer 2

Solving the Inequality: x^2 + 36x < 0

To solve the inequality x^2 + 36x < 0, we need to find the values of x that satisfy the inequality.

Let's break down the problem step by step:

1. Factor the expression x^2 + 36x: - x(x + 36) < 0

2. Determine the critical points: - Set each factor equal to zero and solve for x: - x = 0 - x + 36 = 0 - x = -36

3. Create a sign chart: - We will divide the number line into three intervals: (-∞, -36), (-36, 0), and (0, +∞). - Choose a test point from each interval and evaluate the expression x(x + 36) using the test point. - Determine the sign of the expression in each interval.

| Interval | Test Point | x(x + 36) | |--------------|------------|-----------| | (-∞, -36) | -50 | (-50)(-14) > 0 | | (-36, 0) | -10 | (-10)(26) < 0 | | (0, +∞) | 10 | (10)(46) > 0 |

4. Analyze the sign chart: - The expression x(x + 36) is negative in the interval (-36, 0). - The expression x(x + 36) is positive in the intervals (-∞, -36) and (0, +∞).

5. Determine the solution: - The inequality x^2 + 36x < 0 is satisfied when x is in the interval (-36, 0). - Therefore, the solution to the inequality is -36 < x < 0.

Please note that the solution is exclusive, meaning that x cannot equal -36 or 0.

I hope this helps! Let me know if you have any further questions.