# Maximum value of A1/A2

Calculus Level 4

Let $$a$$ and $$b$$ be two positive real numbers such that $$a+2b\le 1$$. Let $$A_1$$ and $$A_2$$ be, repectively, the areas of circles with radii $$ab^3$$ and $$b^2$$. What is the maximum possible value of $$\dfrac{A_1}{A_2}$$?

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