Least Possible Sum of Recipricols of Two Positive Ints = 9

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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
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The sum of two positive integers is 9. What is the least possible sum of their recipricols?
 
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  • #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.
 

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.

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