Forum
Forums
Questions and Answe...
Algebra
Basics of Algebra
Absolute Value
 
Share:
Notifications
Clear all

[Solved] Absolute Value

 
Basics of Algebra
Last Post by Staff 4 years ago
1 Posts
1 Users
0 Reactions
485 Views
RSS
0
June 14, 2021 5:55 pm
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

|x+4|+|3-x|=10-|y-2|-|1+y|, find the maximum and minimum values of   xy.

Add a comment
1 Answer
0
June 14, 2021 5:55 pm
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

|x+4|+|3-x|=10-|y-2|-|1+y|\Rightarrow |x+4|+|3-x|+|y-2|+|1+y|=10

Since  |x+4|+|3-x|\geqslant 7  and  |y-2|+|1+y|\geqslant 3.   |x+4|+|3-x|+|y-2|+|1+y|=10  only if we choose equal sign in both inequalities. 

|x+4|+|3-x|\geqslant 7 \Rightarrow -4\leqslant x\leqslant 3

|y-2|+|1+y|\geqslant 3\Rightarrow -1\leqslant y\leqslant 2.

Hence  xy  has the maximum value 6 and minimum value -8.

Add a comment
Forum Jump:
  Previous Topic
Share: