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Giải bài 6.27 trang 17 sách bài tập toán 9 - Kết nối tri thức tập 2

Hai chiếc máy bay khởi hành đồng thời từ một sân bay, một chiếc bay theo hướng bắc và chiếc kia bay theo hướng đông (xem hình bên). Chiếc máy bay đi về hướng bắc đang bay nhanh hơn 50 dặm một giờ so với chiếc máy bay đi về hướng đông. Sau 3 giờ, hai máy bay cách nhau 2 440 dặm. Tìm vận tốc của mỗi máy bay.

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Hai chiếc máy bay khởi hành đồng thời từ một sân bay, một chiếc bay theo hướng bắc và chiếc kia bay theo hướng đông (xem hình bên). Chiếc máy bay đi về hướng bắc đang bay nhanh hơn 50 dặm một giờ so với chiếc máy bay đi về hướng đông. Sau 3 giờ, hai máy bay cách nhau 2 440 dặm. Tìm vận tốc của mỗi máy bay.

Phương pháp giải - Xem chi tiết

Các bước giải một bài toán bằng cách lập phương trình:

Bước 1. Lập phương trình:

- Chọn ẩn số và đặt điều kiện thích hợp cho ẩn số. - Biểu diễn các đại lượng chưa biết theo ẩn và các đại lượng đã biết. - Lập phương trình biểu thị mối quan hệ giữa các đại lượng.

Bước 2. Giải phương trình.

Bước 3ꦿ. Trả lời: Kiểm tra xem trong các nghiệm của phương trình, nghiệm nào thỏa mãn điều kiện của ẩn, nghiệm nào không, rồi kết luận.

Lời giải chi tiết

Gọi vận tốc của máy bay đi về hướng đông là x (dặm/ giờ). Điều kiện \(x > 0\). Vận tốc của máy bay đi về hướng bắc là \(x + 50\) (dặm/ giờ). Sau 3 giờ, hai máy bay cách nhau 2 440 dặm nên ta có phương trình: \({\left[ {3\left( {x + 50} \right)} \right]^2} + {\left( {3x} \right)^2} = {2440^2}\) \(18{x^2} + 900x - 5\;931\;100 = 0\) \(9{x^2} + 450x - 2\;965\;550 = 0\) Vì \(\Delta ' = {225^2} - 9.\left( { - 2\;965\;550} \right) = 26\;740\;575\) nên phương trình có hai nghiệm \({x_1} = \frac{{ - 225 + \sqrt {26\;740\;575} }}{9}\) (thỏa mãn) và \({x_2} = \frac{{ - 225 - \sqrt {26\;740\;575} }}{9}\) (không thỏa mãn). Vậy vận tốc của máy bay đi về hướng đông là \(\frac{{ - 225 + \sqrt {26\;740\;575} }}{9}\)(dặm/ giờ) và vận tốc của máy bay đi về hướng bắc là \(\frac{{225 + \sqrt {26\;740\;575} }}{9}\)(dặm/ giờ).

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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