+52 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!
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.
+129852 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)
