greatest value....

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

4 Answers

2305

Shaswata Roy ·2013-03-04 08:49:04

7^724*5^5

2305

Shaswata Roy ·2013-03-04 09:49:41

AM-GM inequality,

2x+3y2â‰¥√6xy
xy â‰¤ 7²2²*6

Weighted AM-GM inequality,

2x+3y5 â‰¥ (x²y³)^1/5

x²y³ â‰¤ 7⁵5⁵

Therefore,

x³y⁴ = x²y³*xy â‰¤ 7⁷5⁵*2²*6

Maximum value of x³y⁴ = 7⁷5⁵*2²*6

1057

Ketan Chandak ·2013-03-04 22:35:57

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 ·2013-03-05 01:39:51

Applying AM-GM

(2x/3+2x/3+2x/3+3y/4+3y/4+3y/4+3y/4)/7â‰¥((2x/3)³(3y/4)⁴)^1/7

This will give you the answer :)

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