So sánh:a)A=26^2-24^2 với B=27^2-25^2 b)A=2021.2023+2023.2025 với B=2020^2+2024^2 13/08/2021 Bởi Natalia So sánh:a)A=26^2-24^2 với B=27^2-25^2 b)A=2021.2023+2023.2025 với B=2020^2+2024^2
Đáp án: $\begin{array}{l}a)A = {26^2} – {24^2}\\ = \left( {26 – 24} \right).\left( {26 + 24} \right)\\ = 2.50\\B = {27^2} – {25^2}\\ = \left( {27 – 25} \right)\left( {27 + 25} \right)\\ = 2.52\\Do:2.50 < 2.52\\ \Rightarrow A < B\\b)A = 2021.2023 + 2023.2025\\ = 2023.\left( {2021 + 2025} \right)\\ = 2023.4046\\ = 2023.2.2023\\ = {2.2023^2}\\B = {2020^2} + {2024^2}\\ \Rightarrow A – B\\ = {2.2023^2} – {2020^2} – {2024^2}\\ = \left( {{{2023}^2} – {{2020}^2}} \right) – \left( {{{2024}^2} – {{2023}^2}} \right)\\ = 4043 – 4047\\ = – 4 < 0\\ \Rightarrow A – B < 0\\ \Rightarrow A < B\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
a)A = {26^2} – {24^2}\\
= \left( {26 – 24} \right).\left( {26 + 24} \right)\\
= 2.50\\
B = {27^2} – {25^2}\\
= \left( {27 – 25} \right)\left( {27 + 25} \right)\\
= 2.52\\
Do:2.50 < 2.52\\
\Rightarrow A < B\\
b)A = 2021.2023 + 2023.2025\\
= 2023.\left( {2021 + 2025} \right)\\
= 2023.4046\\
= 2023.2.2023\\
= {2.2023^2}\\
B = {2020^2} + {2024^2}\\
\Rightarrow A – B\\
= {2.2023^2} – {2020^2} – {2024^2}\\
= \left( {{{2023}^2} – {{2020}^2}} \right) – \left( {{{2024}^2} – {{2023}^2}} \right)\\
= 4043 – 4047\\
= – 4 < 0\\
\Rightarrow A – B < 0\\
\Rightarrow A < B
\end{array}$