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1. Let x and y be positive real numbers such that x + y = xy Find the smallest possible value of x + y.

 

2. For positive real numbers x, y, and z, find the minimum value of

 May 30, 2020
 #1
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-1

1. The minimum value of x + y is 5/4.

 

2. The minimum value is 31, for x = y = z = 1.  Easy!

 May 31, 2020
 #2
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neither of those are correct.

Guest May 31, 2020
 #3
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I realized, sometimes when I post a question, a Guest comes and answers it, but puts no explanation, and they are always wrong.

SpongeBobRules24  May 31, 2020
 #4
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Use symmetry here.  

 

1.  There is nothing to distinguish x from y, so set x = y.  (You should get x + y = 4)

 

2.  Set  25z^3 = 5y^3 = x^3   (You should find a minimum value of 15).

 Jun 1, 2020

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