## Problem Of The Week 29

**Let x,y,z be distinct positive integers such that x+y+z=11. Find the maximum value of (xyz+xy+yz+zx)?**

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For All Your Quant Queries

**Let x,y,z be distinct positive integers such that x+y+z=11. Find the maximum value of (xyz+xy+yz+zx)?**

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Written by Implex

September 27, 2008 at 2:14 am

Posted in Inequalities, Number Thoery, Problem of the week

Tagged with Inequalities, Number Theory, Problem of the week

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The values of x,y,z should be such that the sum is 11 and the products xyz, xy,yz,zx are maximised . Numbers 2,4,5

Value of xyz+xy+yz+zx=78

tyroSeptember 27, 2008 at 3:08 am

good

outtimedSeptember 27, 2008 at 3:25 am

How do we get to this?

Trial and error?.. coz even 4/4/3 seems valid. though it isn’t actually the answer.

Is there any procedure for this?

milindSeptember 27, 2008 at 2:55 pm

4/4/3 is not possible

the integers are distinct

outtimedSeptember 27, 2008 at 3:16 pm