Forum
Forums
Questions and Answe...
Algebra
Quadratic Equations
Absolute Value equa...
 
Share:
Notifications
Clear all

[Solved] Absolute Value equation

 
Quadratic Equations
Last Post by Staff 4 years ago
1 Posts
1 Users
0 Reactions
312 Views
RSS
0
June 15, 2021 10:38 am
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

Find the condition for \alpha such that the equation   |\alpha x-2y-3|+|5x+9|=0   has the solution (x,y)  where  x,y  have the same sign.

Add a comment
1 Answer
0
June 15, 2021 10:38 am
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

\small |\alpha x-2y-3|+|5x+9|=0\Rightarrow \alpha x-2y-3=0.5x+9=0

\small \Rightarrow x=-\frac{9}{5}<0, y=\frac{\alpha x}{2}-\frac{3}{2}=-\frac{9}{10}\alpha -\frac{3}{2}.

Since \small x,y have the same sign,   \small y<0\Rightarrow a>-\frac{5}{3}.

Add a comment
Forum Jump:
  Previous Topic
Next Topic  
Share: