Question
Wed August 29, 2012 By: Vaishnavi

1.

prove that :

Expert Reply
Wed August 29, 2012
We would request you to please ask one question at a time. The solution to your first question is as follows:
 
a2(b+c),b2(c+a),c2(a+b) will in ap
if b2(c+a) - a2(b+c) = c2(a+b) - b2(c+a)
That is, if (b - a) (ab + bc + ca) = (c - b) (ab + bc + ca)
That is, if (b - a) = (c - b)
That is, if 2b = a + c
which is true as a, b, c are in AP
 
Hence, a2(b+c),b2(c+a),c2(a+b) are in ap.
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