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{c^{2}}{a+b}=0[/tex]
[tex]\frac{c}{a+b}+ \frac{a}{b+c}+\frac{b}{a+c}=1 =>a+b+c=(\frac{c}{a+b}+ \frac{a}{b+c}+\frac{b}{a+c})(a+b+c)[/tex]
[tex]=\frac{a^{2}}{b+c}+\frac{b^{2}}{c+a}+\frac{c^{2}}{a+b}+(b+c)\frac{a}{b+c}+(a+c)\frac{b}{a+c}+(a+b)\frac{c}{a+b}=\frac{a^{2}}{b+c}+\frac{b^{2}}{c+a}+\frac{c^{2}}{a+b}+a+b+c[/tex]
[tex]=>\frac{a^{2}}{b+c}+\frac{b^{2}}{a+c}+\frac{c^{2}}{b+b}=0(dpcm)[/tex]