Question

12 <= a <= 17 14 <= b <= 24 Оценить: 1) a+b 2) ab 3) 3a+b

Answer 1

Ответ:

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Answer 2

Based on the given inequalities:

1. To find the minimum and maximum values of the sum (a + b), we need to consider the smallest value of a and the largest value of b within their respective ranges.

The smallest value of a is 12, and the largest value of b is 24. Therefore:

Minimum value of (a + b) = 12 + 24 = 36

Similarly, the largest value of a is 17, and the smallest value of b is 14. Therefore:

Maximum value of (a + b) = 17 + 14 = 31

So, the range of possible values for (a + b) is 36 to 31.

2. To find the minimum and maximum values of the product (ab), we need to consider the smallest values of a and b within their respective ranges.

The smallest value of a is 12, and the smallest value of b is 14. Therefore:

Minimum value of (ab) = 12 * 14 = 168

Similarly, the largest value of a is 17, and the largest value of b is 24. Therefore:

Maximum value of (ab) = 17 * 24 = 408

So, the range of possible values for (ab) is 168 to 408.

3. To find the minimum and maximum values of (3a + b), we need to consider the smallest value of a and the largest value of b within their respective ranges.

The smallest value of a is 12, and the largest value of b is 24. Therefore:

Minimum value of (3a + b) = 3 * 12 + 24 = 60

Similarly, the largest value of a is 17, and the smallest value of b is 14. Therefore:

Maximum value of (3a + b) = 3 * 17 + 14 = 65

So, the range of possible values for (3a + b) is 60 to 65.