\[\eqalign{ & a]\,\,2x\left[ {x - 3} \right] - x\left[ {2x + 3} \right] = 18 \cr & \,\,\,\,\,\,2{x^2} - 6x - 2{x^2} - 3x = 18 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 9x = 18 \cr & x = 18:\left[ { - 9} \right] = - 2 \cr & b]\,\,x\left[ {5{x^2} - 2} \right] + 5x\left[ {1 - {x^2}} \right] = {3^4} \cr & \,\,\,\,\,\,5{x^3} - 2x + 5x - 5{x^3} = 81 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3x = 81 \cr & x = 81:3 = 27 \cr} \]
Đề bài
Tìm x, biết:
a] \[2x[x - 3] - x[2x + 3] = 18\]
b] \[x[5{x^2} - 2] + 5x[1 - {x^2}] = {3^4}\]
Lời giải chi tiết
\[\eqalign{ & a]\,\,2x\left[ {x - 3} \right] - x\left[ {2x + 3} \right] = 18 \cr & \,\,\,\,\,\,2{x^2} - 6x - 2{x^2} - 3x = 18 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 9x = 18 \cr & x = 18:\left[ { - 9} \right] = - 2 \cr & b]\,\,x\left[ {5{x^2} - 2} \right] + 5x\left[ {1 - {x^2}} \right] = {3^4} \cr & \,\,\,\,\,\,5{x^3} - 2x + 5x - 5{x^3} = 81 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3x = 81 \cr & x = 81:3 = 27 \cr} \]