1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# If x,y,z are non negative integers so that x + y + z = 12, then the maximum value of xyz + xy + yz + zx is

A

115

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B

112

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

114/3

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D

111

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is B 112 1.We have(x + 1) (y + 1) (z + 1) = xyz + xy + yz + zx + x + y + z + 1 = xyz + xy + yz + zx + 13; And (x + 1) (y + 1) (z + 1) = 15. Using AM.GM inequality we get xyz + xy + yz + zx + 13 ≤ =125, xyz + xy + yz + zx ≤ 112. Equality holds if x + 1 = y + 1 = z + 1 ; i.e., x = y = z = 4. So the desired maximum is 112. The answer is B.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Inequations I
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program