Please help me in this question Let x, y and z be three non-negative integers such that x+y+z=10. Find the maximum possible value of xyz+xy+yz+zx?? Share with your friends Share 0 Rajat Sethi answered this Taking the 3 no's as : x+1,y+1,z+1A.M ≥ GMx+1 + y+1 +z+13≥ { (x+1)(y+1)(z+1)} 13⇒(133)3 ≥ (x+1)(y+1)(z+1)⇒xyz + xy + yz + zx +x+y+z+1 ≤ (133)3 ⇒xyz + xy + yz + zx ≤ (133)3 -11Equality holds when x = y= z but x+y+z=10 and x,y,z are integers.So, we get maximum value of the expression when any two of x,y,z are equal to 3 and third is equal to 4.Taking x = y = 3 and y = 4xyz + xy + yz + zx = 69 0 View Full Answer
