Question

Chứng minh rằng : nếu \(\frac{a}{b}=\frac{c}{d}\)=> \(\frac{20a+21b}{20c+21d}=\frac{20a-21b}{20c-21d}\)

Answer 1

Ta có: \(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{c}=\frac{b}{d}\)

\(\Leftrightarrow\frac{20a}{20c}=\frac{21b}{21d}\)

Áp dụng tích chất dãy tỉ số bằng nhau ta có :

\(\frac{20a}{20c}=\frac{21b}{21d}=\frac{20a+21b}{20c+21d}=\frac{20a-21b}{20c-21d}\)

Từ        \(\frac{20a+21b}{20c+21d}=\frac{20a-20b}{20c-21d}\)

\(\Leftrightarrow\frac{20a+20b}{20c+21d}=\frac{20a-20b}{20c-20d}\)

                         \(\RightarrowĐpcm\)