Trang chủ » Hỏi đáp » Môn Toán `A=(2022^2022 – 1)/ (2022^2023 – 1 )` và b` = (2020^2021 -1)/(2022^2022-1)` 28/12/2024 `A=(2022^2022 – 1)/ (2022^2023 – 1 )` và b` = (2020^2021 -1)/(2022^2022-1)`
Giải đáp:$A < B$ Lời giải và giải thích chi tiết: $\begin{array}{l}Do:{2022^{2022}} < {2022^{2023}}\\ \Leftrightarrow {2022^{2022}} – 1 < {2022^{2023}} – 1\\ \Leftrightarrow A = \dfrac{{{{2022}^{2022}} – 1}}{{{{2022}^{2023}} – 1}} < 1\\ \Leftrightarrow A = \dfrac{{{{2022}^{2022}} – 1}}{{{{2022}^{2023}} – 1}} < \dfrac{{{{2022}^{2022}} – 1 – 2021}}{{{{2022}^{2023}} – 1 – 2021}}\\ \Leftrightarrow A < \dfrac{{{{2022}^{2022}} – 2022}}{{{{2022}^{2023}} – 2022}}\\ \Leftrightarrow A < \dfrac{{2022.\left( {{{2022}^{2021}} – 1} \right)}}{{2022\left( {{{2022}^{2022}} – 1} \right)}}\\ \Leftrightarrow A < \dfrac{{{{2022}^{2021}} – 1}}{{{{2022}^{2022}} – 1}}\\ \Leftrightarrow A < B\end{array}$ Trả lời
Do:{2022^{2022}} < {2022^{2023}}\\
\Leftrightarrow {2022^{2022}} – 1 < {2022^{2023}} – 1\\
\Leftrightarrow A = \dfrac{{{{2022}^{2022}} – 1}}{{{{2022}^{2023}} – 1}} < 1\\
\Leftrightarrow A = \dfrac{{{{2022}^{2022}} – 1}}{{{{2022}^{2023}} – 1}} < \dfrac{{{{2022}^{2022}} – 1 – 2021}}{{{{2022}^{2023}} – 1 – 2021}}\\
\Leftrightarrow A < \dfrac{{{{2022}^{2022}} – 2022}}{{{{2022}^{2023}} – 2022}}\\
\Leftrightarrow A < \dfrac{{2022.\left( {{{2022}^{2021}} – 1} \right)}}{{2022\left( {{{2022}^{2022}} – 1} \right)}}\\
\Leftrightarrow A < \dfrac{{{{2022}^{2021}} – 1}}{{{{2022}^{2022}} – 1}}\\
\Leftrightarrow A < B
\end{array}$