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if a 2, b 2, c 2 are in A.P. then prove that.. a/b+c, b/c+a, c/a+b

if a2, b2,c2  are in A.P. then  prove that..
a/b+c, b/c+a, c/a+b

Grade:12th pass

3 Answers

dinesh
22 Points
6 years ago
it is very easy 
use b2-a2=c2-b2
 
mycroft holmes
272 Points
6 years ago
If a2, b2, c2 are in A.P., so are a2+ab+bc+ca,  b2+ab+bc+ca, and  c2+ab+bc+ca
 
i.e. (a+b)(c+a), (b+c)(a+b), (c+a)(b+c) are in A.P.
 
Multiplying the three terms by (a+b+c)/ (a+b)(b+c)(c+a), we have
 
(a+b+c)/(b+c), (a+b+c)/c+a, (a+b+c)/a+b are in A.P. Now subtracting 1 from each term, we have
 
1/b+c, 1/c+a, 1/a+b are in A.P.
mycroft holmes
272 Points
6 years ago
If a2, b2, c2 are in A.P., so are a2+ab+bc+ca,  b2+ab+bc+ca, and  c2+ab+bc+ca
 
i.e. (a+b)(c+a), (b+c)(a+b), (c+a)(b+c) are in A.P.
 
Multiplying the three terms by (a+b+c)/ (a+b)(b+c)(c+a), we have
 
(a+b+c)/(b+c), (a+b+c)/c+a, (a+b+c)/a+b are in A.P. Now subtracting 1 from each term, we have
 
1/b+c, 1/c+a, 1/a+b are in A.P.

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