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If (b+c)/a,(c+a)/b,(a+b)/c are in A.P....

If `(b+c)/a,(c+a)/b,(a+b)/c` are in `A.P.` show that `1/a,1/b1/c` are also in `A.P. (a +b+c != 0)`.

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Given `(b+c)/a,(c+a)/b,(a+b)/c` are in `A.P.`
`(c+a)/b-(b+c)/a=(a+b)/c-(c+a)/b`
`=> (ac+a^2-b^2-bc)/ab=(ab+b^2-c^2-ac)/bc`
`=> [(a+b)(a-b)+c(a-b)]/ab=[(b+c)(b-c)+a(b-c)]/bc`
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RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. If a, b, c are in A.P, then show that: b+c-a , c+a-b , a+b-c are in A....

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  2. If a, b, c are in A.P, then show that: b c-a^2, c a-b^2,a b-c^2 are i...

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  3. If (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are als...

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  4. If (b+c)/a ,(c+a)/b ,(a+b)/c are in A.P., prove that : b c ,\ c a ,\ a...

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  5. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

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  6. Insert 3 arithmetic means between 3 and 19.

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  7. For what value of n ,\ dot(a^(n+1)+b^(n+1))/(a^n+b^n) is the arithmeti...

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  8. Between 1 and 31 are inserted m arithmetic mean so that the ratio of t...

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  9. if the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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  10. Find the A.M. between: 7 and 13

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  11. Find the A.M. between: 12\ a n d-8

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  12. Find the A.M. between: (x-y)a n d\ (x+y)

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  13. Insert 4 A.M.s between 4 and 19.

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  14. Insert 7 A.M.s between 2 and 17.

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  15. Insert six A.M.s between 15 and -13.

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  16. There are n A.M.s between 3 and 17. The ratio of the last mean to the ...

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  17. Insert AMs between 7 and 71 such that 5^(th) AM is 27. Also find the n...

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  18. If n A.Ms are inserted between two numbers, prove that the sum of the ...

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  19. Insert five numbers between 8 and 26 such that the resulting sequence ...

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  20. A man saved Rs. 16500 in ten years. In each year after the first he sa...

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