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`

Question

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`

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`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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)`

5 views Answered 2023-02-05 15:29