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Giải bài 2.13 trang 25 sách bài tập toán 9 - Kết nối tri thức tập 1

Chứng minh rằng: Trong ba số tự nhiên liên tiếp thì bình phương số đứng giữa lớn hơn tích hai số còn lại.

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

Toán - Văn - Anh
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Đề bài

Chứng minh rằng: Trong ba số tự nhiên liên tiếp thì bình phương số đứng giữa lớn hơn tích hai số còn lại.

Phương pháp giải - Xem chi tiết

+ Gọi ba số tự nhiên liên tiếp là n, n+1 và n+2. + Chứng minh hiệu \({\left( {n + 1} \right)^2} - n\left( {n + 2} \right) > 0\), từ đó suy ra điều phải chứng minh.

Lời giải chi tiết

Gọi ba số tự nhiên liên tiếp là n, n+1 và n+2. Ta có: \({\left( {n + 1} \right)^2} - n\left( {n + 2} \right) \\= {n^2} + 2n + 1 - {n^2} - 2n = 1 > 0.\) Do đó, \({\left( {n + 1} \right)^2} > n\left( {n + 2} \right)\) Vậy trong ba số tự nhiên liên tiếp thì bình phương số đứng giữa lớn hơn tích hai số còn lại.

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