a+2019/a-2020=b+2019/b-2020 chứng minh a/b =2019/2020 23/07/2021 Bởi Audrey a+2019/a-2020=b+2019/b-2020 chứng minh a/b =2019/2020
Giải thích các bước giải: Ta có: \(\begin{array}{l}\frac{{a + 2019}}{{a – 2020}} = \frac{{b + 2019}}{{b – 2020}}\\ \Leftrightarrow \left( {a + 2019} \right)\left( {b – 2020} \right) = \left( {b + 2019} \right)\left( {a – 2020} \right)\\ \Leftrightarrow ab – 2020a + 2019b – 2019.2020 = ab – 2020b + 2019a – 2019.2020\\ \Leftrightarrow – 2020a + 2019b = – 2020b + 2019a\\ \Leftrightarrow 4039a = 4039b\\ \Leftrightarrow a = b\end{array}\) Bình luận
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\frac{{a + 2019}}{{a – 2020}} = \frac{{b + 2019}}{{b – 2020}}\\
\Leftrightarrow \left( {a + 2019} \right)\left( {b – 2020} \right) = \left( {b + 2019} \right)\left( {a – 2020} \right)\\
\Leftrightarrow ab – 2020a + 2019b – 2019.2020 = ab – 2020b + 2019a – 2019.2020\\
\Leftrightarrow – 2020a + 2019b = – 2020b + 2019a\\
\Leftrightarrow 4039a = 4039b\\
\Leftrightarrow a = b
\end{array}\)