Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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

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

Grade:

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
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
(xyz)^{1/3} <= \frac{(x+y+z)}{3} <= \frac{10}{3}
(xyz) <= [\frac{10}{3}]^3

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,


Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free