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Sir, Let x, y, z be three non-negative integers such that x + y + z = 10. The maximum possible value of xyz + xy + yz + zx is & Can you tell me wich chaper I want to focous to answer this type of questions.

Sir,
Let x, y, z be three non-negative integers such that x + y + z = 10. The maximum possible value of xyz +
xy + yz + zx is
       &
Can you tell me wich chaper I want to focous to answer this type of questions.

Grade:11

1 Answers

Arun
25750 Points
3 years ago
xyz+xy+xz+yz can be expressed as (x + 1)(y + 1)(z + 1) - (x + y + z + 1)
 
Since x+y+z=10
 
xyz+xy+xz+yz = (x + 1)(y + 1)(z + 1) - 11
 
So now we have to maximize
(x + 1)(y + 1)(z + 1) - 11
 
Hello Student, Please find the solution
 
Now x+y+z=10 can be written as (x+1) + (y+1)+ (z+1)=13
 
We can now use AM-GM Rule to get max value, which we will get when value of x+1,y+1 & z+1 is as close as possible (if not equal)
 
Now floor(13/3) = 4 so we can have max value at (4,4,(13-(4+4))
i.e. 4,4,5
 
So Max value = 4*4*5 - 11 = 69

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