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Positive real numbers aaa and bbb are such that a+2b≤1a+2b \leq 1a+2b≤1. Let A1A_1A1 and A2A_2A2 be the areas of circles with radii ab3ab^3ab3 and b2b^2b2 respectively. Find the maximum values of A1A2\dfrac{A_1}{A_2}A2A1.
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