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

Explanation

Here, we know `a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b)` are in AP


Also, `a(1/b + 1/c) + 1, b(1/c + 1/a) + 1, c(1/a + 1/b) + 1` are in AP.


Let us take LCM for each expression then we get, `(ac + ab + bc)/bc , (ab + bc + ac)/ac, (cb + ac + ab)/ab` are in AP.


` 1/(bc), 1/(ac), 1/(ab )`are in AP .


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