Question

a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) are in ap ..Then prove that a,b,c are in AP

Answer 1

given that :-

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

__________

then adding 1 in each number

» a(1/b+1/c)+1 , b(1/c+1/a)+1, c(1/a+1/b)+1 are in AP

And

» a(1/b+1/c)+a/a, b(1/c+1/a)+b/b, c(1/a+1/b)+c/c are in AP

So

» a(1/a+1/b+1/c), b(1/a+1/b+1/c), c(1/a+1/b+1/c) are in AP

__________________________

Divided each term by (1/a+1/b+1/c) we get

=> a, b, c are in AP

______________[PROVED]

===================================