0

Guest

Courses New

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

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

Grade:10

1 Answers

Arun
25750 Points
6 years ago
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)

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More