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Giải bài tập 2.12 trang 37 SGK Toán 9 tập 1 - Kết nối tri thức

Giải các phương trình sau: a) (2left( {x + 1} right) = left( {5x - 1} right)left( {x + 1} right);) b) (left( { - 4x + 3x} right)x = left( {2x + 5} right)x.)

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

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Đề bài

Giải các phương trình sau: a) \(2\left( {x + 1} \right) = \left( {5x - 1} \right)\left( {x + 1} \right);\) b) \(\left( { - 4x + 3} \right)x = \left( {2x + 5} \right)x.\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Chú ý cần đưa phương trình đã cho về phương trình dạng \(A\left( x \right).B\left( x \right) = 0\) thì \(A\left( x \right) = 0\) hoặc \(B\left( x \right) = 0\)

Lời giải chi tiết

a) \(2\left( {x + 1} \right) = \left( {5x - 1} \right)\left( {x + 1} \right)\) \(\begin{array}{l}2\left( {x + 1} \right) - \left( {5x - 1} \right)\left( {x + 1} \right) = 0\\\left( {x + 1} \right)\left( {2 - 5x + 1} \right) = 0\\\left( {x + 1} \right)\left( {3 - 5x} \right) = 0\end{array}\) \(x + 1 = 0\) hoặc \(3 - 5x = 0\) \(x =  - 1\) hoặc \(x = \frac{3}{5}\) Vậy \(x \in \left\{ { - 1;\frac{3}{5}} \right\}.\) b) \(\left( { - 4x + 3} \right)x = \left( {2x + 5} \right)x\) \(\begin{array}{l}\left( { - 4x + 3} \right)x - \left( {2x + 5} \right)x = 0\\x\left( { - 4x + 3 - 2x - 5} \right) = 0\\x\left( { - 6x - 2} \right) = 0\end{array}\) \(x = 0\) hoặc \(-6x - 2 = 0 \) \(x = 0\) hoặc \(x = \frac{{ - 1}}{3}\) Vậy \(x \in \left\{ {0;\frac{{ - 1}}{3}} \right\}.\)

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