+0  
 
0
272
3
avatar+201 

Let \(x,y,z\) be positive real numbers such that \((x \cdot y) + z = (x + z) \cdot (y + z)\). What is the maximum possible value of \(xyz\)?

 Aug 5, 2019
 #1
avatar+6187 
+1

see correction below

.
 Aug 5, 2019
edited by Rom  Aug 5, 2019
 #2
avatar
0

I don't think this is correct

 Aug 5, 2019
 #3
avatar+6187 
+2

You're right.  Not sure what happened.

 

Again using Lagrange multipliers I'm seeing the solution as 

 

x = y = z = 1/3

 

xyz = 1/27

Rom  Aug 5, 2019
edited by Rom  Aug 5, 2019

24 Online Users

avatar