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Giải bài 5 trang 40 vở thực hành Toán 9

Cho (a > b > 0) và (c > d > 0), chứng minh rằng (ac > bd > 0).

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

Toán - Văn - Anh
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Đề bài

Cho \(a > b > 0\) và \(c > d > 0\), chứng minh rằng \(ac > bd > 0\).

Phương pháp giải - Xem chi tiết

+ Với ba số a, b, c ta có: \(a > b\) và \(c > 0\) thì \(ac > bc\). + Nếu \(a > b,b > c\) thì \(a > c\).

Lời giải chi tiết

Từ \(b > 0\) và \(d > 0\) suy ra \(bd > 0\). Từ \(a > b\) nên \(ac > bc\) (do nhân hai vế với \(c > 0\)) (1) Từ \(c > d\) suy ra \(bc > bd\) (do nhân hai vế với \(b > 0\)) (2) Theo tính chất bắc cầu, từ (1) và (2) suy ra \(ac > bd > 0\).

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