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If ab=2a+3b, agt0, b gt0, then the minim...

If `ab=2a+3b, agt0, b gt0`, then the minimum value of ab is

A

12

B

24

C

`(1)/(4)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`ab=2a+3b rArr b=(2a)/(a-3)`
Now `z=ab=(2a^(2))/(a-3)`
`rArr" "(dz)/(da)=(2[(a-3)2a-a^(2)])/((a-3)^(2))=(2[a^(2)-6a])/((a-3)^(2))`
Put `(dz)/(da)=0, therefore a^(2)-6a=0, a=0,6`
Clearly a = 6 is point of minima
when `a=6, b=4 rArr (ab)_("min")=6xx4=24`
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