Áp dụng BĐT gttđ: |a|+|b|\(\ge\) |a+b|
Ta có:A=|1987-3x|+|2718-3x|=|1987-3x|+|3x-2718|\(\ge\) |1987-3x+3x-2718|=|-731|=731
=>AMin=731
Dấu "=" xảy ra\(\Leftrightarrow\left(1987-3x\right)\left(3x-2718\right)\ge0\Leftrightarrow\int^{1987\le3x}_{2718\ge3x}\Leftrightarrow\int^{x\ge}_{x\le906}\frac{1987}{3}\Leftrightarrow\frac{1987}{3}\le x\le906\)
Vậy....