SOLUTION: a/(b+c) + b/(a+c) +c/(a+b)=1 then a^2/(b+c) + b^2/(a+c) +c^2/(a+b) =?

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Question 1035966: a/(b+c) + b/(a+c) +c/(a+b)=1 then a^2/(b+c) + b^2/(a+c) +c^2/(a+b) =?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

a%2F%28b%2Bc%29+%2B+b%2F%28a%2Bc%29+%2Bc%2F%28a%2Bb%29=1

Multiply through by LCD = (b+c)(a+c)(a+b)







 a%5E3%2Babc%2Bb%5E3%2Bc%5E3=0

--------------------

a%5E2%2F%28b%2Bc%29+%2B+b%5E2%2F%28a%2Bc%29+%2Bc%5E2%2F%28a%2Bb%29%22%22=%22%22

%22%22=%22%22

%22%22=%22%22

%22%22=%22%22

Rearrange the terms in the numerator:

%22%22=%22%22

Group: 

%22%22=%22%22 

Factor each group:

%22%22=%22%22 

Since a%5E3%2Babc%2Bb%5E3%2Bc%5E3=0

%28a%280%29%2Bb%280%29%2Bc%280%29%29%2F%28%28a%2Bb%29%28a%2Bc%29%28b%2Bc%29%29%22%22=%22%22

0

Answer: 0

Edwin