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If a/(b+c)+b/(c+a)+c/(a+b),then a2/(b+c)+b2/(c+a)+c2/(a+b)=?

If a/(b+c)+b/(c+a)+c/(a+b),then a2/(b+c)+b2/(c+a)+c2/(a+b)=?

Grade:10

1 Answers

abhilash
19 Points
6 years ago
LET A/B+C=-1,B/C+A=1,C/A+B=1 will satisfy this equation
 
from above,
a= -(b+c),......(1)
b=c+a.....(2)
c=a+b.....(3)
 
now adding equation1,2,3
a+b+c=2a
b+c=a....(4)
 
now a2/b+c=a*(a/b+c)=-a......(5)
 
similarly b2/c+a=b...............(6)
aand
c2/a+b=c.......(7)
 
 
now adding equaation5,6,7
we find desire value
(a2/b+c)+( b2/c+a)+(c2/a+b)=-a+b+c...(8)
 
from equaation 4
b+c=a
 
put value inequation 8
-a+b+c= -a+a=0
 
hence proved
 
 
 

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