Let x, y, z be three non-negative integers such that x+y+z=10 . The maximum possible value of x y z+x y+y z+z x is

Step-by-step solution

Taking three no's. x+1, y+1, z+1 AM GM . (x+1)+(y+1)+(z+1) 3 (x+1)(y+1)(z+1) ^ 1 / 3 ( 13 3 )³ x y z+x y+y z+z x+11 ( 13 3 )³-11 x y z+x y+y z+z x equality hold when x=y=z but x+y+z=0 and x, y, z are integers. So maximum value when any two of x, y, z are equal to 3 and third is equal to 4 .