配套习题- 如何运用绝对值的“几何意义”求最值 -【青果学院】

挑战习题

1/5单选题

难度：

已知|a+b|+|a﹣b|﹣2b=0，在数轴上给出关于a，b的四种位置关系如图所示，则可能成立的有（　　）种

A	1
B	2
C	3
D	4

提示1：: PHA+5qC55o2u57ud5a+55YC855qE5Yeg5L2V5oSP5LmJ55Sx5q+P5Liq5pWw6L205a+5fGErYnwrfGHvuaNifO+5ozJiPTDvvIzov5vooYzliIbmnpDliKTmlq3mmK/lkKbmiJDnq4s8L3A+

正确答案：Qg==

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2/5单选题

难度：

已知a、b、c在数轴上位置如图：则代数式|a|+|a+b|+|c﹣a|﹣|b﹣c|的值等于（　　）

A	﹣3a
B	2c﹣a
C	2a﹣2b
D	b

提示1：: PHA+55SxYe+8jGLvvIxj5Zyo5pWw6L205LiK55qE5a+55bqU5L2N572u5Y+v55+l77yaYu+8nGHvvJww77ycY++8jOWNs+WPr+WIpOaWree7neWvueWAvOespuWPt+WGheaVsOeahOespuWPt++8jOS7juiAjOWOu+aOiee7neWvueWAvOespuWPt++8jOWujOaIkOWMlueugC48L3A+

正确答案：QQ==

PGRpdj48cCBhbGlnbj0ibGVmdCI+6Kej77yafGF8K3xhK2J8K3xj77mjYXzvuaN8Yu+5o2N8Pe+5o2HvuaPvvIhhK2LvvIkr77yIY++5o2HvvIkrYu+5o2M977mjM2E8L3A+PC9kaXY+

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3/5单选题

难度：

在式子|x+1|+|x+2|+|x+3|+|x+4|中，用不同的x值代入，得到对应的值，在这些对应值中，最小的值是（　　）

A	1
B	2
C	3
D	4

提示1：: PHA+5qC55o2u57ud5a+55YC855qE5Yeg5L2V5oSP5LmJ5rGC6KejPC9wPg==

提示2：: 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

正确答案：RA==

PGRpdj48aW1nIHNyYz0iaHR0cHM6Ly9wMS5xaW5nZ3VvLmNvbS9HMS9NMDAvMjMvN0IvckJBQ0UxTU1aZ2Z4QlNoZEFBQVl4amNtMm9JODE3LnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AxLnFpbmdndW8uY29tL0cxL00wMC8yMy83Qi9yQkFDRTFNTVpnZnhCU2hkQUFBWXhqY20yb0k4MTcucG5nIiBhbHQ9IiIgc3R5bGU9IndpZHRoOiA1NjBweDsgaGVpZ2h0OiAxMDdweDsiPjwvZGl2Pg==

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4/5单选题

难度：

当式子|x﹣1|+|x﹣2|+|x﹣3|+…+|x﹣1997|取得最小值时，实数x的值等于（　　）

A	999
B	998
C	1997
D	0

提示1：: 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

正确答案：QQ==

PGRpdj48aW1nIHNyYz0iaHR0cHM6Ly9wMS5xaW5nZ3VvLmNvbS9HMS9NMDAvMDAvOEEvckJBQ0ZGTU1aWnJ3b3ZFMEFBQU5KMWVHV0JjNjcyLnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AxLnFpbmdndW8uY29tL0cxL00wMC8wMC84QS9yQkFDRkZNTVpacndvdkUwQUFBTkoxZUdXQmM2NzIucG5nIiBhbHQ9IiIgc3R5bGU9IndpZHRoOiA0ODJweDsgaGVpZ2h0OiA4M3B4OyI+PC9kaXY+

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5/5单选题

难度：

若y=|x﹣1|+|x﹣2|+|x﹣3|+…+|x﹣19|，y的最小值为（　　）

A	45
B	95
C	90
D	190

提示1：: 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

正确答案：Qw==

PGRpdj48aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvMjMvNzgvckJBQ0UxTU1aUURBRjZqWUFBQVFPbVlaZFdZNDUxLnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8yMy83OC9yQkFDRTFNTVpRREFGNmpZQUFBUU9tWVpkV1k0NTEucG5nIiBhbHQ9IiIgc3R5bGU9IndpZHRoOiA1NTlweDsgaGVpZ2h0OiA2NXB4OyI+PC9kaXY+

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