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dmitriy555 [2]
4 years ago
6

Find two numbers whose difference is 124 and whose product is a minimum. (smaller number) (larger number)

Mathematics
2 answers:
icang [17]4 years ago
8 0
1 and 125

125 - 1 = 124
125 \times 1 = 125
good luck
Galina-37 [17]4 years ago
3 0

For this case, the first thing we must do is define variables.

We have then:

x: unknown number 1

y: unknown number 2

The difference of both numbers is 124:

x - y = 124

The product of both numbers is:

P = x * y

Writing the product based on a variable we have:

P (x) = x * (x-124)

Rewriting:

P (x) = (x ^ 2-124x)

To find the minimum of the function, we must derive:

P '(x) = 2x-124

We equal zero and clear x:

2x-124 = 0\\2x = 124\\x = 124/2\\x = 62

Then, the value of the other number is given by:

y = x-124\\y = 62-124\\y = -62

Answer:

The searched numbers that meet both conditions are:

smaller number = 62

larger number = -62

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