+0

0
272
3
+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
+6187
+1

see correction below

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

I don't think this is correct

Aug 5, 2019
#3
+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