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a²/(b+c) + b²/(c+a) + c²/(a+b) = 0. Prove that a/(b+c) + b/(c+a) + c/(a+b) = 1.

a²/(b+c) + b²/(c+a) + c²/(a+b)  = 0.
Prove that a/(b+c) + b/(c+a) + c/(a+b) = 1.
 

Grade:10

1 Answers

Arun
25750 Points
5 years ago
 
Dear student
 
take a/(b+c) +b/(c+a) +c/(a+b) =1
 
then multiply (a+b+c)  in both the sides
a(a+b+c) / (b+c) + b(a+b+c) / (a+c) + c(a+b+c) / (b+a) = a+b+c
 
a2 / (b+c)  + a(b+c)/ (b+c)  + b2 / (c+a) + b(c+a)/ (c+a)  +  c2 / (a+b)  + c(a+b)/ (a+b) = a+b+c
 
a2 / (b+c)  + a + b2 / (c+a) + b  +  c2 / (a+b)  + c = a+b+c
 
a2 / (b+c)  + b2 / (c+a) +  c2 / (a+b)  = 0
 
hope it helps

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