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if ab=2a+3b, a>0,b>0 then the min. value of ab=? (plz tell the answer by using inequalities and also differentiation and by any simple method u have)thnku...

if ab=2a+3b, a>0,b>0 then the min. value of ab=?


(plz tell the answer by using inequalities and also differentiation  and by any simple method u have)thnku... 

Grade:10

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear ajinkya

ab=2a+3b ...............1

use AM ≥GM

 (2a+3b)/2  ≥ (6ab)1/2

 or  (2a+3b)  ≥ 2(6ab)1/2

 so from equation 1

 ab ≥ 2(6ab)1/2

 (ab)1/2 ≥ 2(6)1/2

ab ≥ 24

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