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Find two positive numbers that satisfy the given requirements.

The product is 154, and the sum is a minimum.

(Enter your answers as a comma-separated list.)

Sagot :

GinnyAnsweridn
To solve this problem, we need to find two positive numbers whose product is 154 and whose sum is minimized. Let's work through the steps:

1. Identify Factors:
We need to find pairs of factors for 154. Factors are numbers that multiply together to get 154. Here are the pairs of factors of 154:
- 1 and 154
- 2 and 77
- 7 and 22
- 11 and 14

2. Calculate Their Sums:
For each pair of factors, calculate their sum:
- The sum of 1 and 154 is [tex]\(1 + 154 = 155\)[/tex].
- The sum of 2 and 77 is [tex]\(2 + 77 = 79\)[/tex].
- The sum of 7 and 22 is [tex]\(7 + 22 = 29\)[/tex].
- The sum of 11 and 14 is [tex]\(11 + 14 = 25\)[/tex].

3. Find the Minimum Sum:
Among the sums calculated, the minimum sum is:
- [tex]\(155\)[/tex]
- [tex]\(79\)[/tex]
- [tex]\(29\)[/tex]
- [tex]\(25\)[/tex]

We can see that the smallest sum is [tex]\(25\)[/tex].

4. Identify Corresponding Pair:
The pair of factors corresponding to the minimum sum [tex]\(25\)[/tex] is [tex]\(11\)[/tex] and [tex]\(14\)[/tex].

5. Conclusion:
Therefore, the two positive numbers whose product is 154 and whose sum is minimized are [tex]\(11\)[/tex] and [tex]\(14\)[/tex].

Thus, the answer is [tex]\(11, 14\)[/tex].
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