Question

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

Answer 1

1 and 125

$125 - 1 = 124$
$125 \times 1 = 125$
good luck

Answer 2

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