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If a+b 2 , b, b+c 2 are in HP, then which one of the following is correct?

Options

  1. Aa, b, c are in AP
  2. Ba, b, c are in GP
  3. Ca+b, b+c, c+a are in GP
  4. Da+b, b+c, c+a are in AP

Correct answer

B. a, b, c are in GP

Step-by-step solution

a+b 2 , b, b+c 2 are in H.P 2 b = 2 a+b + 2 b+c = 2(a+2 b+c) (a+b)(b+c) aligned & (a+b)(b+c)=b(a+2 b+c) & a b+c a+b^2+b c=a b+2 b^2+b c & b^2=c a aligned a, b, c are in G.P.

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