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Giải Bài 45 trang 54 sách bài tập toán 7 tập 1 - Cánh diều

Cho tỉ lệ thức

🎃Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

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

Cho tỉ lệ thức \(\dfrac{x}{2} = \dfrac{y}{7}\) và \(xy = 56\). Tìm x và y.

Phương pháp giải - Xem chi tiết

Nếu \(\dfrac{a}{b} = \dfrac{c}{d} \) thì \(ad = bc\).

Lời giải chi tiết

Ta có: \(\dfrac{x}{2} = \dfrac{y}{7} \) suy ra \( x = \dfrac{y}{7}.2 = \dfrac{{2y}}{7}\). Thay \(x = \dfrac{{2y}}{7}\) vào \(xy = 56\) ta được: \(\begin{array}{l}xy = 56\\ \dfrac{{2y}}{7}.y = 56\\ \dfrac{{2{y^2}}}{7} = 56\\ \dfrac{2}{7}.{y^2} = 56\\ {y^2} = 56:\dfrac{2}{7} = 196\end{array}\) Suy ra \(y = \pm 14\) Với \(y = 14\) thì \(x = 56:14 = 4\). Với \(y =  - 14\) thì \(x = 56:( - 14) =  - 4\). Vậy \(x = 4,{\rm{ }}y = 14\) hoặc \(x =  - 4,{\rm{ }}y =  - 14\).

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