Least Possible Sum of Recipricols of Two Positive Ints = 9

[Itachi]

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

 

[matt grime]

you can do it by listing all the possibilities, that'll show you what the general pattern is.

 

[mathman]

1/4 + 1/5. The general formala simply says make the numbers as equal as possible.

 

[quddusaliquddus]

Oh man! ... mathman..I italic[jus] worked that out!...was about to post it!..oh well...:D

 

[Gokul43201]

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?"

 

[HallsofIvy]

A square with each side of length perimeter/4.

 

[robert Ihnot]

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.