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Giải bài 8 trang 72 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Giải các phương trình chứa căn thức sau: a) \(\sqrt {3{x^2} - 4x + 1} = \sqrt {{x^2} - x} \) b) \(\sqrt {6{x^2} - 11x - 3} = 2x - 1\)

Tổng hợp đề thi học kì 2 lớp 10 tất cả c💟ác môn - Kết nối tri thức

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Đề bài

Giải các phương trình chứa căn thức sau:  a) \(\sqrt {3{x^2} - 4x + 1}  = \sqrt {{x^2} - x} \) b) \(\sqrt {6{x^2} - 11x - 3}  = 2x - 1\)

Phương pháp giải - Xem chi tiết

Bước 1: Bình phương hai vế của PT Bước 2: Giải PT thu được Bước 3: Thử lại và KL nghiệm

Lời giải chi tiết

a) \(\sqrt {3{x^2} - 4x + 1}  = \sqrt {{x^2} - x} \)\(\begin{array}{l} \Rightarrow 3{x^2} - 4x + 1 = {x^2} - x\\ \Leftrightarrow 2{x^2} - 3x + 1 = 0\\ \Leftrightarrow (x - 1)(2x - 1) = 0\\ \Leftrightarrow \left[ \begin{array}{l}x = 1\\x = \frac{1}{2}\end{array} \right.\end{array}\)Thử lại ta thấy PT đã cho có nghiệm duy nhất \(x = 1\)b) \(\sqrt {6{x^2} - 11x - 3}  = 2x - 1\)\(\begin{array}{l} \Rightarrow 6{x^2} - 11x - 3 = {\left( {2x - 1} \right)^2}\\ \Leftrightarrow 6{x^2} - 11x - 3 = 4{x^2} - 4x + 1\\ \Leftrightarrow 2{x^2} - 7x - 4 = 0\\ \Leftrightarrow \left[ \begin{array}{l}x = 4\\x =  - \frac{1}{2}\end{array} \right.\end{array}\)Thử lại ta thấy PT đã cho có nghiệm duy nhất \(x = 4\)

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