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Let x and y be real numbers such that xy=9 Find the set of all possible values of x+y

 May 24, 2021
 #1
avatar+2407 
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I think since sqrt(9) = +- 3, it can be all numbers other than -6 to 6  (non inclusive)

 

=^._.^=

 May 24, 2021
 #2
avatar+178 
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Use AM-GM for positive x,y, we can get that x+y>=6, and for negatives x+y<=-6.

 

So, it is either x+y>=6 or x+y<=-6.

 May 24, 2021

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