To find the possible values of a that satisfy the given equations, we can solve the system of equations:
a + ab^2 = 250b ...(1)
a - ab^2 = -240b ...(2)
Let's eliminate the variable 'ab^2' by subtracting equation (2) from equation (1):
(a + ab^2) - (a - ab^2) = 250b - (-240b)
Simplifying, we have:
2ab^2 = 250b + 240b
2ab^2 = 490b
ab^2 = 245b
Now, we can divide both sides of the equation by b (assuming b is non-zero):
ab^2 / b = 245b / b
a b = 245
So, we have found that the value of ab must be 245.
To find the possible values of a, we need to consider the possible values of b. Since the question does not provide any constraints or additional information about b, we can assume that b can take any non-zero real value.
Therefore, for any non-zero real value of b, the corresponding value of a can be calculated by dividing 245 by b:
a = 245 / b
In conclusion, all possible values of a are given by the expression 245 / b, where b is a non-zero real number.
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