Cho [TEX]\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=1[/TEX] CMR: [TEX]\frac{a^{2}}{b+c}+\frac{b^{2}}{c+a}+\frac{a^{2}}{a+b}=0[/TEX]
[tex]\frac{a^{2}}{b+c}+\frac{b^{2}}{a+c}+\frac{c^{2}}{a+b} =a\left (\frac{a}{b+c} +1-1 \right)+ b\left (\frac{b}{a+c} +1-1 \right)+ c\left (\frac{c}{a+b} +1-1 \right) = \left ( a+b+c \right )\left (\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \right )-a-b-c= 0[/tex]