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

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