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if x,y,z are natural numbers then what is maximum value of xyz+xy+yz

if x,y,z are natural numbers then what is maximum value of xyz+xy+yz

Grade:12

3 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
There has to be some relation or a bound/condition to the question, otherwise this would be just void. So, send in the complete and question typed correctly.
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Souvik Chaki
24 Points
6 years ago
this was asked by kvpy in 2013
-_- so i think u should be abale to answer it and noting wrong in the question
mycroft holmes
272 Points
6 years ago
The missing condition is that x+y+z = 10.
 
Now, if the numbers were non-negative real numbers, then all we would have to do is use the AP-GP inequality, and in that case the maximum would have happened at x=y=z=10/3. Here x,y,z are natural numbers. So our surest way of maximizing the expression is to therefore choose x,y,z as close to 10/3. Hence we are guided to the triplet (3,3,4) and the expression evaluates to 69

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