x是有理数，求|x-100/22
x是有理数，求y = |x - 100/221| + |x + 95/221|的最小值。
1、当x≥100/221时
y = |x - 100/221| + |x + 95/221|
= x - 100/221 + x + 95/221
= 2x - 5/221
当x = 100/221时取得最小值
ymin = 2×100/221 - 5/221 = 15/17
2、当-95/221≤x＜100/221时
y = |x - 100/221| + |x + 95/221|
= -x + 100/221 + x + 95/221
= 195/221
= 15/17
3、x＜-95/221...全部
x是有理数，求y = |x - 100/221| + |x + 95/221|的最小值。
1、当x≥100/221时
y = |x - 100/221| + |x + 95/221|
= x - 100/221 + x + 95/221
= 2x - 5/221
当x = 100/221时取得最小值
ymin = 2×100/221 - 5/221 = 15/17
2、当-95/221≤x＜100/221时
y = |x - 100/221| + |x + 95/221|
= -x + 100/221 + x + 95/221
= 195/221
= 15/17
3、x＜-95/221时
y = |x - 100/221| + |x + 95/221|
= 100/221 - x - x - 95/221
= -2x + 5/221
当x = -95/221时取得最小值
ymin = 2×95/221 + 5/221 = 285/17
所以y = |x - 100/221| + |x + 95/221|的最小值为
ymin = 15/17。收起
