SOLUTION: For x and y positive integers, if xy > = 9, what is the smallest possible sum of x + y?

Question 1111386: For x and y positive integers, if xy > = 9, what is the smallest possible sum of x + y?
Answer by ikleyn(52792) (Show Source): You can put this solution on YOUR website!
.

x + y =  +  =  + .


This line is an IDENTITY.


Now, the term    is ALWAYS positive (non-negative), therefore, we can continue and transform this line / identity in THIS WAY


x + y =  +  =  +   > =   =  = 2*3 = 6.


Thus we have established this inequality


x + y >= 6.


Taking x= y= 3,  we get the exact value  of 6  for  x+y.  


In all other cases we have inequality  x + y > 6.


So, under the given condition  xy >= 9,  the smallest value for  x + y  is  6.

SOLVED.

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