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viva [34]
3 years ago
9

Of all the numbers whose difference is 36​, find the two that have the minimum product

Mathematics
1 answer:
scZoUnD [109]3 years ago
8 0

Answer:

54,18

Step-by-step explanation:

Let one of the numbers be x. The other number be represented as 36-x

(x-(36-x ) = 36

open brackets

x - 36 + x  =  36

x + x = 36+ 36 = 72

2x = 72

x = 72/2 = 36

x =  36

The product can then be represented as y = x(36-x) or y=36x-x²

 The maximum or minimum is always on the axis of symmetry which has the formula x=-b/2a.

In our case, the axis of symmetry is -36/-2, so x=18.

 

If one number is 18 and the 2 numbers differentiate by 36, the other number is 18 + 36 = 54

So the 2 numbers are 18 and 54 and the minimum product is 972

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Two consecutive positive integers have a product of 6. what are the integers
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Hey there!

One way to do this is find all the factors of 6 and then see which pair fit the requirements.

The factors of 6 are 1, 2, 3, and 6. (Note: There can be negative factors, but I am going to leave them out since it is asking for positive integers.)

You can find them by asking if each number can go into 6.

1, 2, 3, and 6 all go into 6, while 4 and 5 do not.

The requirements we have is that they must be consecutive <u>and</u> have a product of 6.

Consecutive means right after one another.

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