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Giải bài 6 trang 10 SGK Toán 10 tập 2 – Chân trời sáng tạo

Một khung dây thép hình chữ nhật có chiều dài 20 cm và chiều rộng 15 cm được uốn lại thành hình chữ nhật mới có kích thước

Tổng hợp đề thi học kì 2 lớp 1𒅌0 tất cả các môn - Chân trời sáng tạo

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Đề bài

Một khung dây thép hình chữ nhật có chiều dài 20 cm và chiều rộng 15 cm được uốn lại thành hình chữ nhật mới có kích thước \(\left( {20 + x} \right)\) cm và \(\left( {15 - x} \right)\) cm. Với x nằm trong các khoảng nào th🐻ì diện tích của khung sau khi uốn: tăng lên, không thay đổi, giảm đi?

Phương pháp giải - Xem chi tiết

Bước 1: Lập hiệu giữa diện tích mới và diện tích cũ \(f\left( x \right) = 20.15 - \left( {20 + x} \right)\left( {15 - x} \right)\) với \(x > 0\) Bước 2: Tìm các khoảng thỏa mãn yêu cầu           +) Khoảng mà \(f\left( x \right) > 0\) là khoảng diện tích tăng lên           +) Khoảng mà \(f\left( x \right) < 0\) là khoảng diện tích giảm đi           +) Khoảng mà \(f\left( x \right) = 0\) là khoảng diện tích không đổi

Lời giải chi tiết

Theo giải thiết ta có tam thức sau: \(f\left( x \right) = 20.15 - \left( {20 + x} \right)\left( {15 - x} \right) =   {x^2} + 5x\)Tam thức có \(\Delta  = 25 > 0\), có hai nghiệm phân biệt \({x_1} = 0;{x_2} = -5\)Vậy khoảng diện tích tăng lên là \(x>0\) và \(x<-5\), khoảng diện giảm đi là \(x \in(-5;0)\) và diện tích không đổi khi \(x = 0\) và \(x = -5\)

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