Expert: Sherry Wallin - 1/4/2009

Question
Heres the equations
a = square root of (b + c)
c = a^2 - e
a = d - c
e = d + c
a = (d + e)/b

Questions:
How do you know you have enough information to solve the
problem?
How can you tell if the problem is paradoxical?
What is the procedure for solving a problem like this?

Answer
This is in response to your question a = b^2, b = a - b:

substitute a = b^2 into b = a-b getting b = b^2-b. Now subtract b from both sides getting b^2-2b = 0 and factor getting b(b-2) = 0. Now you know that b = 0 or b-2 = 0 so b = 0, 2. So there is a solution. Plug in b== 0 into a = b^2 getting a = 0 and b = 2 getting a = 4. You can check the values a = 0 and b = 0 and a = 4 and b = 2 to see both solutions work so this is a consistent system, i.e., non- paradoxical, non- contradictory.

Hi Joshua~
    I have to play around with this a bit but for now to answer your question about how do you know if the problem is paradoxical you need to derive logical statements that follow from each of your premises (statements above). For example you can solve for a^2 and get that c + e = a^2. You can substitute for e in the c = a^2-e with the statement
e = d + c. What you will be looking for is a contradiction. You might get that a = 2 and a = sqrt2 which cannot ever be true, then you know it is paradoxical and that it can not be solved. I will look for that contradiction but try it.

Math Prof

If you haven't figured it out send another request please and I will help you more.

Hi  Joshua~
   When you want to ask another question please send it in another request. I am unable to send a response to an additional question so I am appending it to this question.