Question
If 1b−a+1b−c = 1a+1c, then a,b,c are in
Answer: Option C
:
C
Since the reciprocals of a and c occur on RHS, let us first assume that a,b,c are in H.P.
So that 1a,1b,1c are in A.P.
⇒1b−1a = 1c−1b = d,say
⇒a−bab = d = b−cbc⇒a−b = abd and b - c =bcd
Now LHS = −1a−b+1b+c = −1abd+1bcd
=1bd(1c−1a) = 1bd(2d)∴2b = 1a+1c = RHS
∴ a, b, c are in H.P. is verified.
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:
C
Since the reciprocals of a and c occur on RHS, let us first assume that a,b,c are in H.P.
So that 1a,1b,1c are in A.P.
⇒1b−1a = 1c−1b = d,say
⇒a−bab = d = b−cbc⇒a−b = abd and b - c =bcd
Now LHS = −1a−b+1b+c = −1abd+1bcd
=1bd(1c−1a) = 1bd(2d)∴2b = 1a+1c = RHS
∴ a, b, c are in H.P. is verified.
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