Q. 83.8( 5 Votes )

are in A.P., show that are in A.P. provided a + b + c 0

Answer :

Given: are in AP





Taking LCM


b2c + c2b + a2b + ab2 – 2ac2 – 2a2c = 0


b2c + c2b + a2b + ab2 –ac2 – ac2 – a2c – a2c = 0


(b2c – a2c) + (c2b – ac2) + (a2b – a2c) + (ab2 – ac2) = 0


c (b – a)(b + a) + c2(b – a) + a2 (b – c) + a(b + c)(b – c) = 0


c(b – a) {(b + a) + c} + a(b – c) {a + (b + c)} = 0


(a + b + c){cb – ca + ab – ca} = 0


Given a + b + c ≠ 0


cb – ca + ab – ca = 0


cb – 2ca + ab = 0




are in AP


Hence Proved


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