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Giải mục 1 trang 6, 7, 8 Chuyên đề học tập Toán 10 - Chân trời sáng tạo

Ba lớp 10A, 10B, 10C gồm 128 học sinh cùng tham gia lao động trồng cây. Mỗi học sinh lớp 10A trồng được 3 cây bạch đàn và 4 cây bàng

ꦏTổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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HĐ khám phá 1

Ba lớp 10A, 10B, 10C gồm 128 học sinh cùng tham gia lao động trồng cây. Mỗi học sinh lớp 10A trồng được 3 cây bạch đàn và 4 cây bàng. MIỗi học sinh lớp 10B trồng được 2 cây bạch đàn và 5 cây bàng. Mỗi học sinh lớp 10C trồng được 6 cây bạch đàn. Cả 3 lớp trồng được 476 cây bạch đàn và 375 cây bàng. Gọi x, y, = lần lượt là số học sinh của các lớp 10A, 10B,10C. a) Lập các hệ thức thể hiện mối liên hệ giữa x, y và z. b) Trong bảng dữ liệu sau, chọn các số liệu phủ hợp với số học sinh của mỗi lớp 10A, 10B, 10C và giải thích sự lựa chọn của bạn.

Lời giải chi tiết:

a) Ba lớp có 128 học sinh nên \(x + y + z = 128\) Số cây bạch đàn mà 3 lớp trồng được là: \(3x + 2y + 6z = 476\) Số cây bàng mà 3 lớp trồng được là: \(4x + 5y = 375\) b) Số liệu phù hợp là số liệu thỏa mãn cả 3 liên hệ liệt kê ở ý a). \(x = 41,y = 43,z = 44\) sai vì số cây bàng là \(4.41 + 5.43 = 379 \ne 375\) \(x = 40,y = 43,z = 45\) thỏa mãn cả 3 liên hệ trên. \(x = 42,y = 43,z = 43\) sai vì số cây bàng là \(4.42 + 5.43 = 383 \ne 375\) Vậy số liệu phù hợp với số học sinh mỗi lớp là \(x = 40,y = 43,z = 45\)

Thực hành 1

Hệ nào dưới đây là hệ phương trình bậc nhất ba ẩn? Mỗi bộ ba số (1; 5; 2), (1;1;1) và (-1; 2; 3) có là nghiệm của hệ phương trình bậc nhất ba ẩn đó không? (1) \(\left\{ \begin{array}{l}4x - 2y + z = 5\\4xz - 5y + 2z =  - 7\\ - x + 3y + 2z = 3\end{array} \right.\)            (2) \(\left\{ \begin{array}{l}x + 2z = 5\\2x - y + z =  - 1\\3x\; - 2y =  - 7\end{array} \right.\)

Phương pháp giải:

Bộ ba số là nghiệm của hệ nếu nó thỏa mãn cả 3 phương trình của hệ.

Lời giải chi tiết:

Hệ phương trình (1) không phải là hệ phương trình bậc nhất vì phương trình thứ hay chứa \(xz\) Hệ phương trình (2) là hệ phương trình bậc nhất ba ẩn. +) Bộ ba số (1; 5; 2) là nghiệm của hệ phương trình (2) vì \(\left\{ \begin{array}{l}  1 + 2.2 = 5\\2.1 - 5 + 2 =  - 1\\3.1 - 2.5 =  - 7\end{array} \right.\) (nghiệm đún cả ba phương trình của hệ). +) Bộ ba số (1;1;1) không là nghiệm của hệ phương trình (2) vì \(2.1 - 1 + 1 = 2 \ne  - 1\) (không là nghiệm của phương trình \(2x - y + z =  - 1\)) +) Bộ ba số (-1; 2; 3) là nghiệm của hệ phương trình (2) vì \(\left\{ \begin{array}{l} - 1 + 2.3 = 5\\2.( - 1) - 2 + 3 =  - 1\\3.( - 1) - 2.2 =  - 7\end{array} \right.\) (nghiệm đún cả ba phương trình của hệ).

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