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105
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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.

 Mar 30, 2021
 #1
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0

Elimnating y, we get x^2 = 1225.  So the possible values of x are 35 and -35.

 Mar 30, 2021
 #2
avatar+121004 
+1

x + xy^2  =    250y

x -  xy^2  =  - 240y         add  these

 

2x  = 10y

x = (10/2) y

x = 5y                 sub this  back  into the first equation

 

5y + 5yy^2 = 250y           divide  though by 5y   

 

1 + y^2  =  50

 

y^2  = 49               take both roots

 

y =    -7            or     y  =  7 

 

x = 5(-7)  =  -35               x = 5(7)  =  35   

 

And   (x, y)  =  (0,0)  is a trivial solution

 

So

 

x =  35, 0 , 35

 

cool cool cool

 Mar 30, 2021

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