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.
(ive came up with 35 and -35, but it isnt correct)
+129850 You're close.....just one more solution
x + xy^2 = 250y
x - xy^2 = -240 y add these
2x = 10y
x = (10/2) y
x = 5y sub into the first equation
5y + (5y)y^2 = 250y
5y^3 = 250y - 5y
5y^3 = 245y { here's where you might have dropped a solution by dividing out y }
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
y = 0 ⇒ x = 5(0) = 0
y = -7 , x = -35
y = 7 , x = 35
