Question

[Bảo Uyên Ngô]

a/(b+c)+b/(c+a)+c/(a+b)=1 cmr (a^2)/(b+c)+(b^2)/(c+a)+(c^2)/(a+b)=0

Answer 1

[Lầy Văn Lội]

\(a+b+c=\left(a+b+c\right)\left(\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\right)\)

\(=\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}+\frac{ab}{a+c}+\frac{ac}{a+b}+\frac{ab}{b+c}+\frac{bc}{a+b}+\frac{ac}{b+c}+\frac{bc}{a+c}\)

\(=\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}+a+b+c\)

\(\Rightarrow\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}=0\)