# Bài 9 trang 18 Tài liệu dạy – học Toán 8 tập 1

Đề bài

Tìm x, biết:

a) $(x - 5)(x + 2) + (x + 1)(2 - x) = 15$

b) $(2x - 3)(x + 5) - (x - 2)(2x + 1) = 3$

Lời giải chi tiết

\eqalign{ & a)\,\,\left( {x - 5} \right)\left( {x + 2} \right) + \left( {x + 1} \right)\left( {2 - x} \right) = 15 \cr & \,\,\,\,\,\,{x^2} + 2x - 5x - 10 + 2x - {x^2} + 2 - x = 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2x - 8 = 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2x = 23 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 23:\left( { - 2} \right) \Leftrightarrow x = - 11,5 \cr & b)\,\,\left( {2x - 3} \right)\left( {x + 4} \right) - \left( {x - 2} \right)\left( {2x + 1} \right) = 3 \cr & \,\,\,\,\,\,\left( {2{x^2} + 10x - 3x - 15} \right) - \left( {2{x^2} + x - 4x - 2} \right) = 3 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10x - 13 = 3 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10x = 3 + 13 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10x = 16 \Leftrightarrow x = 1,6 \cr & \cr}

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