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

Hello Student,

use the flg concept

AM >= GM >= HM
x+y+z=10
so xyz+xy+yz+zx
= xyz(1+ 1/x + 1/y + 1/z) ….…...(1)

Now GM<=AM



Similarily
HM <= AM
1/x + 1/y + 1/z <= x+y+z <= 10

Now put this values in equation (1)
Hope this was helpful
Thanks,