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Let a and b be two positive real numbers...

Let a and b be two positive real numbers such that `a + 2b<=1`. Let `A_1` and `A_2` be, respectively, the areas of circles with radii `ab^3` and `b^2`. Then the maximum possible value of `A_1/A_2` is:

A

`1/16`

B

`1/64`

C

`1/(16sqrt2)`

D

`1/32`

Text Solution

Verified by Experts

The correct Answer is:
b
`a+2ble1`
`A_(1) =pia^(2)b^(6)`
`A_(2)=pib^(4)`
`Rightarrow (A_(1))/(A_(2))=a^(2)b^(2)`
`& 1& 1ge2bge2sqrt(2ab)(AMgeGM)`
`1ge2sqrt(2ab)`
`1ge4.2ab`
`Rightarrow1/64gea^(2)b^(2)`
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