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Mathematics

New kid on the Block

 Joined: 10 Mar 2010 Post: 2
10 Mar 2010 12:01:09 IST
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a/b+c,b/c+a,c/a+b are in HP show that a,b,c are in HP
CBSE Board , CBSE X , Mathematics

a/b+c,b/c+a,c/a+b are in HP show that a,b,c are in HP

New kid on the Block

Joined: 10 Mar 2010
Posts: 2
10 Mar 2010 12:02:51 IST
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New kid on the Block

Joined: 4 Apr 2010
Posts: 10
7 Apr 2010 19:47:06 IST
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That's really easy :-

given, a/(b+c) , b/(c+a) , c/(a+b) are in H.P
=> (b+c)/a , (c+a)/b , (a+b)/c are in A.P
Adding 1 to all the terms
(b+c)/a + 1, (c+a)/b + 1, (a+b)/c + 1 will also be in A.P
=> (a+b+c)/a , (a+b+c)/b, (a+b+c)/c will also be in A.P
On dividing each terms by (a+b+c)
1/a,1/b,1/c will also be in A.P
=> a,b,c are in H.P

Forum Expert
Joined: 19 Oct 2006
Posts: 7797
30 May 2012 18:01:50 IST
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Since a/b+c, b/c+a, c/a+b are in H.P.

⇒ b+c/a, c+a/b, a+b/c are in A.P.

⇒ a+b+c/a, a+b+c/b, a+b+c/c are in A.P.

⇒ 1/a, 1/b, 1/c are in A.P.

a, b, c are in H.P.

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