回復 11# floot363 的帖子
複選題9.
若\(\displaystyle \frac{b+c}{2a}=\frac{a-c}{2b}=\frac{a-b}{2c}\)，求\(\displaystyle \frac{a}{a+b+c}\)的值？(A)1 (B)\(-1\) (C)\(\displaystyle \frac{1}{2}\) (D)\(\displaystyle -\frac{1}{2}\)
[解答]
供大家參考，請大家指教。
\(\displaystyle \frac{b+c}{2a}=\frac{a-c}{2b}=\frac{a-b}{2c}=k\)
\(\displaystyle a=\frac{b+c}{2k},b=\frac{a-c}{2k},c=\frac{a-b}{2k}\)
\(\displaystyle \frac{a}{a+b+c}=k\)
\(\cases{\displaystyle a+b+c=\frac{a}{k}\cr b+c=2ak}\)
\(\displaystyle a+2ak=\frac{a}{k}\)
\(2k^2+k-1=\)
\((2k-1)(k+1)=0\)
\(\displaystyle k=\frac{1}{2}\)或\(k=-1\)
