Question

Cho dãy tỉ số bằng nhau

a/b+c = b/a+c = c/a+b

Tính D = a/ b+c + b/a+c + c/a+b

Mình đang cần gấp nhờ m.n giúp mình

Answer 1

\(\dfrac{a}{b+c}=\dfrac{b}{a+c}=\dfrac{c}{a+b}\\ \Rightarrow\dfrac{a}{b+c}+1=\dfrac{b}{a+c}+1=\dfrac{c}{a+b}+1\\ \Rightarrow\dfrac{a+b+c}{b+c}=\dfrac{a+b+c}{a+c}=\dfrac{a+b+c}{a+b}\)

+) Nếu a+b+c=0

\(\Rightarrow\left\{{}\begin{matrix}a+b=-c\\b+c=-a\\a+c=-b\end{matrix}\right.\\ \Rightarrow D=\dfrac{a}{-a}+\dfrac{b}{-b}+\dfrac{c}{-c}=-1+-1+-1=-3\)

+) Nếu a+b+c khác 0

\(\Rightarrow b+c=a+c=a+b\\ \Rightarrow a=b=c\\ \Rightarrow D=\dfrac{a}{2a}+\dfrac{b}{2b}+\dfrac{c}{2c}=\dfrac{a+b+c}{2\left(a+b+c\right)}=\dfrac{1}{2}\)