Luyện tập 4 trang 20 Tài liệu dạy – học Toán 8 tập 1

Đề bài

Tìm x, biết:

a) \((5x - 2)(5x + 2) - (5x + 3)(5x - 4) = 8\) ;

b) \((4x - 3)(4x + 2) + (4x + 5)(1 - 4x) = {2.5^2}\)

Lời giải chi tiết

\(\eqalign{  & a)\,\,\left( {5x - 2} \right)\left( {5x + 2} \right) - \left( {5x + 3} \right)\left( {5x - 4} \right) = 8  \cr  & \,\,\,\,\,25{x^2} - 4 - \left( {25{x^2} - 20x + 15x - 12} \right) = 8  \cr  & \,\,\,\,\,\,\,\,\,25{x^2} - 4 - 25{x^2} + 20x - 15x + 12 = 8  \cr  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5x + 8 = 8  \cr  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5x = 0  \cr  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0  \cr  & b)\,\,\left( {4x - 3} \right)\left( {4x + 2} \right) + \left( {4x + 5} \right)\left( {1 - 4x} \right) = {2.5^2}  \cr  & \,\,\,\,\,\,16{x^2} + 8x - 12x - 6 + 4x - 16{x^2} + 5 - 20x = 50  \cr  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 20x - 1 = 50  \cr  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 20x = 51  \cr  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x =  - {{51} \over {20}} \cr} \)