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Grade: 10
        If a/(b+c)+b/(c+a) +c/(a+b)=1 then prove that a^2/(b+c)+b^2/(c+a)+c^2/(a+b)=0
5 months ago

Answers : (1)

Arun
11634 Points
							
Dear student
 
 
\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 $\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b} = 0$
 
 
Hope it helps
 
 
If you find any difficulty please feel free to ask.
 
Regards
Arun (askIITians forum expert)
5 months ago
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