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If 1 b+c , 1 c+a , 1 a+b are in HP, then Which of the following is/are correct? 1. a, b, c are in AP 2. (b+c)^2,(c+a)^2,(a+b)^2 are in GP Select the correct answer using the code given below.

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

1 b+c , 1 c+a , 1 a+b are in H.P. b+c, c+a, a+b are in A.P. Subtract a+b+c -a,-b,-c , are also in A.P. a, b, c , are also in A.P. So, statements 1 is correct. Let a=a, b=a+d, c=a+2 d aligned & [(c+a)^2 ]^2=(2 a+2 d)^4=16(a+d)^4 & (b+c)^2 (a+b)^2=(2 a+3 d)^2(2 a+d)^2 & (c+a)^4 (b+c)^2 (a+b)^2 aligned so, (b+c)^2,(c+a)^2,(a+b)^2 are not in G.P so, statements-2 is not correct.

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