Least Possible Sum of Recipricols of Two Positive Ints = 9

  • Thread starter Itachi
  • Start date
In summary, the conversation discusses finding the least possible sum of reciprocals of two positive integers whose sum is 9. The general formula is to make the numbers as equal as possible, with the closest values being 4 and 5. The conversation also briefly mentions maximizing the area of a rectangle given its perimeter, with the optimal solution being a square with each side being the perimeter divided by 4.
  • #1
Itachi
11
0
The sum of two positive integers is 9. What is the least possible sum of their recipricols?
 
Physics news on Phys.org
  • #2
you can do it by listing all the possibilities, that'll show you what the general pattern is.
 
  • #3
1/4 + 1/5. The general formala simply says make the numbers as equal as possible.
 
  • #4
Oh man! ... mathman..I italic[jus] worked that out!...was about to post it!..oh well...:D
 
  • #5
Itachi said:
The sum of two positive integers is 9. What is the least possible sum of their recipricols?

OR "given the perimeter of a rectangle, how do you maximize its area?"
 
  • #6
A square with each side of length perimeter/4.
 
  • #7
I guess you could write 1/x + 1/(9-x) =s, differentiate and set equal to zero getting:

x^2 = (9-x)^2. The maximal value is x=0, and the minimal value is x=4.5, or they are the same. So 4 and 5 are the closest.
 

FAQ: Least Possible Sum of Recipricols of Two Positive Ints = 9

What is the equation for finding the least possible sum of reciprocals of two positive integers when their product is equal to 9?

The equation is 1/x + 1/y = 9, where x and y are positive integers.

What is the smallest possible sum of reciprocals of two positive integers that can equal 9?

The smallest possible sum is when x = 1 and y = 9, or when x = 3 and y = 3. Both of these combinations give a sum of 1 + 1/9 = 9.

What are the possible integer solutions for the equation 1/x + 1/y = 9?

The possible integer solutions are (1,9), (9,1), (3,3). These are the only combinations of positive integers that give a sum of 9.

Can the equation 1/x + 1/y = 9 have any negative integer solutions?

No, the equation only has positive integer solutions. The sum of two negative numbers cannot equal 9.

How can the equation 1/x + 1/y = 9 be solved to find the values of x and y?

The equation can be rearranged to y = 9x/(x-9). By substituting different values for x, the corresponding value for y can be found. For example, when x = 1, y = 9. When x = 2, y = -18. By trying different values for x, the possible integer solutions can be found.

Similar threads

I Meaning of terms in a direct sum decomposition of an algebra
Replies
8
Views
2K
Each integer n>11 can be written as the sum of two composite numbers?
Replies
7
Views
3K
MHB How Do You Solve the Equation 183997272.140609=SUM((X/PI())/SQRT(9)/16)?
Replies
2
Views
1K
Proof in number theory: the sum of all divisors of n
Replies
12
Views
1K
Game theory: dice game to aim for sum no greater than 9
Replies
11
Views
3K
MHB Sum of Two Subspaces and lub - Roman, Chapter 1, page 39
Replies
2
Views
1K
I Probability of Sum of 2 Random Ints Being Prime
Replies
6
Views
1K
I Probability to get a certain number or less by throwing two 6-faced die
Replies
6
Views
2K
B How to pick some numbers out of 13 integers, by a 4 digits code
Replies
4
Views
1K
MHB S8.3.7.4. The sum of two positive numbers is 16.
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top