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Question

If a2,b2,c2 are in A.P. then the following are also in A.P. True or False? If true write 1 otherwise write 0 ab+c,bc+a,ca+b.

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Solution

Assume ab+c,bc+a,ca+b. are in A.P
bc+aab+c=ca+bbc+a
(bc+a+1)(ab+c+1)=(ca+b+1)(bc+a+1)
1c+a1b+c=1a+b1c+a
bab+c=cba+b
b2a2=c2b22b2=a2+c2
Hence our assumption is True.
Thus answer is 1.

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