Question -
Answer -
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 foreach 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 arein AP
Let us multiplynumerator with ‘abc’, we get
abc/bc, abc/ac, abc/abare in AP
∴ a, b, c are in AP.
Hence proved.