Question

Решите неравенство x*(3-x)>0 *- УМНОЖЕНИЕ

Answer 1

x=0          x=0               x=0
-x+3=0     -x=-3\:(-1)     x=3

Методом интервалов находим что х принадлежит (0;3)

Answer 2

To solve the inequality x*(3-x) > 0, we can use a method called the sign chart or interval notation. This method involves finding the values of x that make the expression positive or negative.

Step 1: Find the critical points

To find the critical points, we set the expression x*(3-x) equal to zero and solve for x. In this case, we have: x*(3-x) = 0

Solving this equation, we find two critical points: x = 0 and x = 3.

Step 2: Create a sign chart

Next, we create a sign chart by dividing the number line into three intervals based on the critical points: (-∞, 0), (0, 3), and (3, +∞).

Step 3: Test the intervals

For each interval, we choose a test point and substitute it into the expression x*(3-x). We then determine whether the expression is positive or negative.

For the interval (-∞, 0), we can choose x = -1 as a test point. Substituting x = -1 into the expression x*(3-x), we get (-1)*(3-(-1)) = (-1)*(3+1) = (-1)*4 = -4. Since the result is negative, the expression x*(3-x) is negative in this interval.

For the interval (0, 3), we can choose x = 1 as a test point. Substituting x = 1 into the expression x*(3-x), we get (1)*(3-1) = (1)*(2) = 2. Since the result is positive, the expression x*(3-x) is positive in this interval.

For the interval (3, +∞), we can choose x = 4 as a test point. Substituting x = 4 into the expression x*(3-x), we get (4)*(3-4) = (4)*(-1) = -4. Since the result is negative, the expression x*(3-x) is negative in this interval.

Step 4: Determine the solution

Based on the sign chart, we can determine the solution to the inequality x*(3-x) > 0. The solution is the union of the intervals where the expression is positive. In this case, the solution is (0, 3).

Therefore, the solution to the inequality x*(3-x) > 0 is 0 < x < 3.

Please note that this solution is based on the assumption that x is a real number.