+0  
 
+1
97
4
avatar+50 

been struggling on this one

 

Real numbers x and y satisfy

 

\(\begin{align*} x + xy^2 &= 250y, \\ x - xy^2 &= -240y. \end{align*}\)

 

Enter all possible values of x, separated by commas.

 

 

 

Thanks!

 Apr 17, 2021
 #1
avatar
0

You can add and subtract the equations.  Then this gives you that the solutions x are 35 and -35, and the soluitons y are 7 and -7.

 Apr 17, 2021
 #2
avatar+121004 
+1

x + xy^2  =  250y

x - xy^2  = -240 y

 

Add these  and  we  get  that

 

2x  = 10y

x  = (10/2) y  =  5y

 

Sub this  into the  first equation and  we  get

 

5y + (5y)y^2  = 250y

 

5y^3 - 245y  =  0

 

y^3  - 49y  = 0

 

y ( y^2  - 49)  = 0

 

y (y + 7) ( y - 7) =  0

 

Setting all three factors to 0 and solving for y  gives us that

 

y= 0   and x =5(0) =  0

y = -7  and x = 5(-7)  = -35

y =7  and x =5(7)  = 35

 

So....the solutions are  ( x,y)  = (0,0)   (-35 , -7)   and (35 , 7)

 

cool cool cool

 Apr 17, 2021
 #3
avatar+50 
+1

Thanks!

Chocolatehere  Apr 17, 2021
 #4
avatar+121004 
+1

Ur  Welcome   !!!

 

 

cool cool cool

CPhill  Apr 17, 2021

10 Online Users

avatar
avatar