Question

1. Cho \(\frac{^a1}{^a2}=\frac{^a2}{^a3}=\frac{^a3}{^a4}=...=\frac{^a8}{^a9}=\frac{^a9}{^a1}\)và \(\left(^a1+^a2+...+^a9\ne0\right)\)

Chứng minh : \(^a1=^a2=^a3=...=^a9\)

2. Cho tỉ lệ thức : \(\frac{a+b+c}{a+b-c}=\frac{a-b+c}{a-b-c}\)và \(b\ne0\)

Chứng minh c=0

Answer 1

\(\frac{a+b+c}{a+b-c}=\frac{a-b+c}{a-b-c}=\frac{a+b-c+2c}{a+b-c}=\frac{a-b-c+2c}{a-b-c}=1+\frac{2c}{a+b-c}=1+\frac{2c}{a-b-c}\)

\(\Leftrightarrow\frac{2c}{a+b-c}=\frac{2c}{a-b-c}\Leftrightarrow\orbr{\begin{cases}c=0\\a+b-c=a-b-c\end{cases}\Leftrightarrow\orbr{\begin{cases}c=0\\b-c=-b-c\end{cases}\Leftrightarrow}\orbr{\begin{cases}c=0\\b=0\left(loai\right)\end{cases}}}\)

câu 1 thì b áp dụng t.c là ra