|x+2|+|x-1|=9-|y+1|-|y-5|求x+y的最大值与最小值.

题目

|x+2|+|x-1|=9-|y+1|-|y-5|求x+y的最大值与最小值.

答案

=Ix+2I+Ix-1I+Iy-5I+Iy+1I
≥Ix+2+x-1I+Iy-5+y+1I
=I2x+1I+I2y-4I
≥I2x+2y-3I
所以-9≤2x+2y-3≤9
-3≤x+y≤6
所以x+y的最大值为6,最小值为-3