Algebra
If a,b,c are in A.P. and a^2, b^2, c^2 are in H.P., then show that c = a + b.(Question from Sequence and Series).
If a,b,c are in A.P. and a^2, b^2, c^2 are in H.P., then show that c = a + b.
(Question from Sequence and Series).
1 Answer
Arun
Please find the answer to your question
Given that a, b, c are in A. P.
⇒ 2b = a + c ……. (1)
And a2, b2, c2 are in H. P.
⇒ 
⇒ (a – b)(a + b)/b2a2 = (b – c) (b + c)/b2c2
⇒ ac2 + bc2 = a2b + a2c [∵ a – b = b – c]
⇒ ac (c – a) + b (c – a) (c + a) = 0
⇒ (c – a) (ab + bc + ca) = 0
⇒ either c – a = 0 or ab + bc + ca = 0
⇒ either c = a or (a+ c) b + ca = 0 2
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algebra
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