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Giải bài 12 trang 34 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Cho a,b là hai số thực dương sao cho a > b. Chứng minh rằng (frac{1}{a} < frac{1}{b}).

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

Toán - Văn - Anh
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Đề bài

Cho a,b là hai số thực dương sao cho a > b. Chứng minh rằng \(\frac{1}{a} < \frac{1}{b}\).

Phương pháp giải - Xem chi tiết

Dựa vào: Tính chất liên hệ giữa thứ tự và phép nhân: Cho ba số a, b, c. Nếu a > b: *Nếu c > 0 thì a.c > b.c; *Nếu c < 0 thì a.c < b.c; Các tính chất trên vẫn đúng với các bất đẳng thức có dấu <, \( \ge ,\)\( \le \).

Lời giải chi tiết

Nhân hai vế của a > b với \(\frac{1}{{ab}}\), ta được \(\frac{1}{a} < \frac{1}{b}\).

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