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Giải bài 10 trang 12 sách bài tập toán 8 - Cánh diều

Tìm ba số tự nhiên liên tiếp, biết tích của hai số sau lớn hơn tích của hai số trước là 12 đơn vị.

ꦏTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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

Tìm ba số tự nhiên liên tiếp, biết tích của hai số sau lớn hơn tích của hai số trước là 12 đơn vị.

Phương pháp giải - Xem chi tiết

Để nhân hai đơn thức, ta có thể làm như sau: + Nhân các hệ số với nhau và nhân các phần biến với nhau + Thu gọn đơn thức nhận được ở tích.

Lời giải chi tiết

Gọi ba số tự nhiên liên tiếp cần tìm là \(a,a + 1,a + 2\). Do tích của hai số sau lớn hơn tích của hai số trước là 12 đơn vị nên \(\left( {a + 1} \right)\left( {a + 2} \right) - a\left( {a + 1} \right) = 12\).Ta có: \(\left( {a + 1} \right)\left( {a + 2} \right) - a\left( {a + 1} \right) \\= {a^2} + 2a + a + 2 - {a^2} - a \\= 2a + 2\)Do đó: \(2a + 2 = 12\). Suy ra \(a = 5\).Vậy ba số tự nhiên cần tìm là 5,6,7.

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