mycroft holmes
Last Activity: 10 Years ago
We have (a+b+c)[ (a/b+c) + (b/c+a) + (c/a+b) ] = a^2/(b+c)+b^2/(c+a)+c^2/(a+b) + (a+b+c)
Hence if (a/b+c) + (b/c+a) + (c/a+b) =1, the equation becomes
a+b+c = a^2/(b+c)+b^2/(c+a)+c^2/(a+b) + (a+b+c)
so that a^2/(b+c)+b^2/(c+a)+c^2/(a+b) = 0