+1725 Real numbers $a$ and $b$ satisfy
a + ab^2 = 250ab + ab^3
a - ab^2 = 240ab - 50b^2
Enter all possible values of a, separated by commas.
+129771 Trivial solution (a,b) = (0,0)
a + ab^2 = 250ab + ab^3
a - ab^2 = 240ab - 50b^2 add these and then subtract them
2a = 490ab + ab^3 - 50b^2
2ab^2 = 10ab + ab^3 + 50b^2 add these
2a + 2ab^2 = 500ab + 2ab^3 divide through by a
2 + 2b^2 = 500b + 2b^3
1 + b^2 = 250b + b^3
b^3 - b^2 + 250b - 1 = 0
b ≈ .004
a ≈ -.02
