If b is the harmonic mean between a and c, prove that ;1/b-a + 1/b-c=1/a+1/c.

Asked by  | 6th Jul, 2008, 11:29: PM

Expert Answer:

since b is H.M. of a and c so  2/b= 1/a +1/c

so R.H.S. = 2/b

in L.H.S. = ( 2b-a-c ) / (b2 - (a+c)+ac )

now put  b= 2ac /(a+c) and simplify it

you will get the same thing.

Hence the given relation is proved.

Answered by  | 10th Aug, 2008, 08:56: PM

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