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Giải bài 4 trang 27 SGK Toán 8 tập 1 - Cánh diều

Chứng tỏ rằng:

🥂Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Chứng tỏ rằng: \(a)M = {32^{2023}} - {32^{2021}}\) chia hết cho 31 b) \(N = {7^6} + {2.7^3} + {8^{2022}} + 1\) chia hết cho  8

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Phân tích M thành tích của các số trong đó có một số chia hết cho 31. Phân tích N thành tích của các số trong đó có một số chia hết cho 8.

Lời giải chi tiết

\(\begin{array}{l}a)M = {32^{2023}} - {32^{2021}}\\M = {32^{2021}}\left( {{{32}^2} - 1} \right)\\M = {32^{2021}}.1023\end{array}\)

꧒Vì \(1023 \vdots 31\) nên \(M = \left( {{{32}^{2021}}.1023} \right) \vdots 31\)

Vậy M chia hết cho 31.

ꦗ\(\begin{array}{l}b)N = {7^6} + {2.7^3} + {8^{2022}} + 1\\N = {\left( {{7^3}} \right)^2} + {2.7^3} + 1 + {8^{2022}}\\N = {\left( {{7^3} + 1} \right)^2} + {8^{2022}}\\N = {\left( {344} \right)^2} + {8^{2022}}\\N = {\left( {8.43} \right)^2} + {8^{2022}}\\N = {8^2}\left( {{{43}^2} + {8^{2020}}} \right)\end{array}\)

🥂Vì \({8^2} \vdots 8\) suy ra \(N = {8^2}\left( {{{43}^2} + {8^{2020}}} \right) \vdots 8\)

Vậy N chia hết cho 8

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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