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Giải bài 2.14 trang 37 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Tìm x để \(2x,3x + 2\) và \(5x + 3\) là các số hạng liên tiếp của một cấp số cộng.

🌠Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Tìm x để \(2x,3x + 2\) và \(5x + 3\) là các số hạng liên tiếp của một cấp số cộng.

Phương pháp giải - Xem chi tiết

Nếu \({u_1},{u_2},{u_3}\) là ba số hạng liên tiếp của cấp số cộng \(\left( {{u_n}} \right)\) thì \({u_1} + {u_3} = 2{u_2}\)

Lời giải chi tiết

Vì \(2x,3x + 2\) và \(5x + 3\) là các số hạng liên tiếp của một cấp số cộng nên \(2x + 5x + 3 = 2\left( {3x + 2} \right) \Leftrightarrow 7x + 3 = 6x + 4 \Leftrightarrow x = 1\)Thử lại, ta có ba số tìm được là 2, 5, 8 thỏa mãn bài toán. Vậy \(x = 1\)

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