roveマbitve ,Telia ,1t4b are also in AP, - , are also in A.P

1.	roveマbitve ,Telia ,1t4b are also in AP, - , are also in A.P
Answer» A, b, c ... in AP. ∴ 2b = a + c .......... (1) ∴ To Prove : 1/(√b + √c), 1/(√c + √a), 1/(√a + √b) ... in AP ⇒ To Prove : [ 1/(√c+√a) ] - [ 1/(√b+√c) ] = [ 1/(√a+√b) ] - [ 1/(√c+√a) ] ⇒ To Prove : [ (√b-√a) / (√b+√c) ] = [ (√c-√b) / (√a+√b) ] ⇒ To Prove : (√b-√a)·(√b+√a) = (√c-√b)·(√c+√b) ⇒ To Prove : b - a = c - b ⇒ To Prove : 2b = a + c, which is True ... from (1) Hence, the result.

Answer»

A, b, c ... in AP.

∴ 2b = a + c .......... (1)

∴ To Prove : 1/(√b + √c), 1/(√c + √a), 1/(√a + √b) ... in AP

⇒ To Prove : [ 1/(√c+√a) ] - [ 1/(√b+√c) ] = [ 1/(√a+√b) ] - [ 1/(√c+√a) ]

⇒ To Prove : [ (√b-√a) / (√b+√c) ] = [ (√c-√b) / (√a+√b) ]

⇒ To Prove : (√b-√a)·(√b+√a) = (√c-√b)·(√c+√b)

⇒ To Prove : b - a = c - b

⇒ To Prove : 2b = a + c, which is True ... from (1)

Hence, the result.

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