Question

if a,b,c are in A.P then prove that 1/√b+√c ,1/√c+√a ,1/√a+√b are in A.P​

Answer 1

Step-by-step explanation:

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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