Question

مطلوب است محاسبه $$ \frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} $$ درصورتی که: $$a+b+c=7 \wedge \frac{1}{a+b} + \frac{1}{b+c} + \frac{1}{a+c} = \frac{7}{10}$$

Answer 1

$\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b}=A \Longrightarrow A+3=(a+b+c) \big(\frac{1}{a+b} + \frac{1}{b+c} + \frac{1}{a+c} \ \big)=7× \frac{7}{10} \Rightarrow A= \frac{19}{10} $