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