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

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

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Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
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 ) / (b^2 - (a+c)+ac )
now put  b= 2ac /(a+c) and simplify it
you will get the same thing.
Hence the given relation is proved.

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