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Real numbers a and b satisfy

a + ab^2 = 250b,
a - ab^2 = -240b.
Enter all possible values of a, separated by commas.

2 Answers

3 votes

Answer: 20, -10

Step-by-step explanation: To solve the given system of equations, we can use the method of substitution. By rearranging the first equation, we have a = 250b - ab^2. Substituting this expression for a in the second equation, we get 250b - ab^2 - ab^2 = -240b. Simplifying further, we have 250b - 2ab^2 = -240b. Rearranging this equation, we get 250b + 240 = 2ab^2. Combining like terms, we have 490b = 2ab^2.

User Charroch
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4 votes

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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User Alex Huszagh
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8.3k points