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Let a ,b be positive real numbers. If a ...

Let `a ,b` be positive real numbers. If `a A_1, A_2, b` be are in arithmetic progression `a ,G_1, G_2, b` are in geometric progression, and `a ,H_1, H_2, b` are in harmonic progression, show that `(G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)=((2a+b)(a+2b))/(9a b)`

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To solve the problem, we need to show that: \[ \frac{G_1 G_2}{H_1 H_2} = \frac{A_1 + A_2}{H_1 + H_2} = \frac{(2a + b)(a + 2b)}{9ab} \] ### Step 1: Understanding the Progressions ...
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Knowledge Check

  • Let A_1 , A_2 …..,A_3 be n arithmetic means between a and b. Then the common difference of the AP is

    A
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    B
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    C
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    D
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