greatest value....

The greatest value of x3y4 if 2x+3y=7 and x, y ≥ 0

4 Answers

2305
Shaswata Roy ·

7^724*5^5

2305
Shaswata Roy ·

AM-GM inequality,

2x+3y2≥√6xy
xy ≤ 7222*6

Weighted AM-GM inequality,

2x+3y5 ≥ (x2y3)1/5

x2y3 ≤ 7555

Therefore,

x3y4 = x2y3*xy ≤ 7755*22*6

Maximum value of x3y4 = 7755*22*6

1057
Ketan Chandak ·

that's the thing man....i got the same thing...answer given is 32/3.You are close to the wrong but still maybe it's wrong.

1357
Manish Shankar ·

Applying AM-GM

(2x/3+2x/3+2x/3+3y/4+3y/4+3y/4+3y/4)/7≥((2x/3)3(3y/4)4)1/7

This will give you the answer :)

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