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\(Real numbers $a$ and $b$ satisfy \begin{align*} a + ab^2 &= 250b, \\ a - ab^2 &= -240b. \end{align*}Enter all possible values of $a,$ separated by commas. \)

 Jun 20, 2023
edited by Guest  Jun 20, 2023
 #1
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To solve for a, we can subtract the two equations given in the problem. This gives us:

2ab^2 = 90b ab^2 = 45b b(a - 45) = 0

This means that either b = 0 or a - 45 = 0.

If b = 0, then a = 0.

If a - 45 = 0, then a = 45.

Therefore, the possible values of a are 0 and 45.

 Jun 20, 2023
 #3
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a + ab^2 ==250b,   

a - ab^2= - 240b, solve for a, b

 

a = -35,  0,  35
 

Guest Jun 20, 2023
 #4
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Yeah the second guest is right.

Guest Jun 20, 2023
 #5
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If someone doesn't understand something, then it's right to help them. Some of us are nice enough to answer these questions if we know the answer. Personally, I answer because I love math, and spreading that knowledge is great. You don't have to be so rude about it. Sometimes people need help. And it's not cheating or anything, sometimes people just don't get a problem. It's fine to ask for help. You don't have to be so rude. You can keep your opinion to yourself, but posting it here is different. 

 Jun 21, 2023

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