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KVPY2016MathematicsCircle

Let a and b be two positive real numbers such that a+2 b 1 . Let A₁ and A₂ be, respectively, the areas of circles with radii ab ³ and b ² . Then the maximum possible value of A ₁ ~A ₂ is

Options

  1. A1 16
  2. B1 64
  3. C1 16 2
  4. D1 32

Correct answer

B. 1 64

Step-by-step solution

a+2 b 1A₁= a² b⁶A₂= b⁴ A₁ A₂ =a² b² & 1 a+2 b 2 2 a b (A M G M) 1 2 2 a b 1 4-2 a b 1 64 a² b²

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