We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
134
3
avatar+166 

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+6045 
+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+6045 
+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

11 Online Users

avatar