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Giải bài 6 trang 30 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Cho a, b, c, d là các số thực thoả mãn a > b và c > d. a) Chứng minh: a + c > b + d. b) a – c > b – d có luôn luôn đúng không? Nếu không, hãy cho ví dụ.

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

Toán - Văn - Anh
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Đề bài

ꦚCho a, b, c, d là các số thực thoả mãn a > b và c > d.

a) Chứng minh: a + c > b + d.

🐬b) a – c > b – d có luôn luôn đúng không? Nếu không, hãy cho ví dụ.

Phương pháp giải - Xem chi tiết

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

Lời giải chi tiết

a) Cộng c và hai vế của a > b ta được a + c > b + c (1) Cộng b vào hai vế của c > d ta được c + b > d + b  (2) Từ (1) và (2) suy ra a + c > b + d. b) a – c > b – d không phải luôn luôn đúng. Ví dụ: Lấy a = 10, b = 9, c = 5, d = 1, ta có: 10 > 9 và 5 > 1. Tuy nhiên 10 – 5 < 9 – 1.

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

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