已知丨x+2丨+丨1-x丨=10-丨y-5 丨-丨1+y丨,求x+y的最小值取值范围
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已知丨x+2丨+丨1-x丨=10-丨y-5 丨-丨1+y丨,求x+y的最小值取值范围
已知丨x+2丨+丨1-x丨=10-丨y-5 丨-丨1+y丨,求x+y的最小值取值范围
已知丨x+2丨+丨1-x丨=10-丨y-5 丨-丨1+y丨,求x+y的最小值取值范围
|x + 2| + |1 - x| = 10 - |y - 5| - |1 + y|
(1) x ≤ -2,y ≤ -1:
- (x + 2) + (1 - x) = 10 + (y - 5) + (1 + y)
-2x - 1 = 2y + 6
x + y = -7/2
(2) x ≤ -2,-1 < y ≤ 5:
- (x + 2) + (1 - x) = 10 + (y - 5) - (1 + y)
-2x - 1 = 4
x = -5/2
-7/2 < x + y ≤ 5/2
(3) x ≤ -2,y > 5:
- (x + 2) + (1 - x) = 10 - (y - 5) - (1 + y)
-2x - 1 = -2y + 14
x - y = -15/2
5/2 < x + y ≤ 7/2
(4) -2 < x ≤ 1,y ≤ -1:
(x + 2) + (1 - x) = 10 + (y - 5) + (1 + y)
3 = 2y + 6
y = -3/2
-7/2 < x + y ≤ -1/2
(5) -2 1,y ≤ -1:
(x + 2) - (1 - x) = 10 + (y - 5) + (1 + y)
2x + 1 = 2y + 6
x - y = 5/2
无解
(8) x > 1,-1 < y ≤ 5:
(x + 2) - (1 - x) = 10 + (y - 5) - (1 + y)
2x + 1 = 4
x = 3/2
1/2 < x + y ≤ 13/2
(9) x > 1,y > 5:
(x + 2) - (1 - x) = 10 - (y - 5) - (1 + y)
2x + 1 = -2y + 14
x + y = 13/2
当x = -5/2,y = -1 或 x = -2,y = -3/2时:x + y = -7/2
好的加分啊问题补充:要有过程啊 不是要最大值吗?要看取值范围 你六年级的应该这样理把B,C,F,G,坐标代入到x+y 得出答案!
x+y的最小值为-3.5
祝你好运