Let a and b be two positive real numbers such that a+2b≤1. Let A1 and A2 be respectively, the areas of circles with radii ab3 and b2. Then the maximum possible value of A1A2 is
A
116
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B
164
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C
116√2
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D
132
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Solution
The correct option is B164 a+2b≤1A1=πa2b6,A2=πb4⇒A1A2=a2b21≥a+2b≥2√2ab(∵AM≥GM)⇒1≥2√2ab⇒1≥4×2ab⇒1≥64a2b2⇒164≥a2b2