Home » Ask & Discuss » Class X
« Back to Discussion

Mathematics

New kid on the Block

Joined:	10 Mar 2010
Post:	2

10 Mar 2010 12:01:09 IST

0 People liked this

475

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

Comments (3)

ravi

New kid on the Block

Joined: 10 Mar 2010

Posts: 2

10 Mar 2010 12:02:51 IST

Like 0 people liked this

Shall get answer

Aamir Khan

New kid on the Block

Joined: 4 Apr 2010

Posts: 10

7 Apr 2010 19:47:06 IST

Like 0 people liked this

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
which is the required answer

edison

Forum Expert

Joined: 19 Oct 2006

Posts: 7797

30 May 2012 18:01:50 IST

Like 0 people liked this

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.

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team