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Problem of Tartaglia (1500-1557): among all positive numbers a, b whose sum is 12, find those for which the product of the two numbers and their difference is largest

Respuesta :

jhonyy9
1+11=12
2+10=12
3+9=12
4+8=12
5+7=12
6+6=12

so the product and their difference is largest so these are 2 and 10 with product equal 20 and difference of 8 

hope this will help you 

To solve this problem we have to consider all the possible pairs of sum 12

any pair of  numbers that satisfies equation (1) will be under observation

[tex]\rm a+b =\ 12 .....(1)[/tex]

{a,b}

has following possible pairs

1. { 11 , 1}

2, { 10 ,2 }

3. { 9 , 3}

4. { 8 , 4 }

5. { 7 , 5}

6. { 6 ,6}

Differences are given by

1 . 10

2.  8

3.  6

4.  4

5.   2

6.   0

Products are given by

1 . 11

2.  20

3.  27

4.  32

5.  35

6.  36

We can clearly see from the above observations that Difference of two numbers is largest for Pair 2. { 10 ,2 }

Also

From the above observations that Product of  two numbers is largest for Pair 6. { 6,6 }

For more information please refer to  the link below

https://brainly.com/question/17429689

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