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Grade: 10
        If a/(b+c)+b/(c+a)+c/(a+b)=1,then a2/(b+c)+b2/(c+a)+c2/(a+b)=?
3 years ago

Answers : (1)

jagdish singh singh
173 Points
							
\hspace{-.7 cm}$Given $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} = 1\;,$ Multiply both side by $a+b+c$\\\\\\ So $\bigg(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\bigg)\cdot (a+b+c)=a+b+c$\\\\\\ $\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}+\frac{a(b+c)}{b+c}+\frac{b(c+a)}{c+a}+\frac{c(a+b)}{a+b}=a+b+c$\\\\\\ So we get $\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b} = 0$
3 years ago
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