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Math Help - Forming simultaneous equations from the following?

  1. #1
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    Forming simultaneous equations from the following?

    Form a pair of simultaneous equations and solve them to find x and y, given they are rational numbers.

    Questions 1: x-3+√(y+2) = -1 + √5




    Question 2: 1 1/2 + √(x+2y) = 3x + y + 2/3√3

    Any help is appreciated
    Those are 2 separate questions.
    Last edited by D7236; April 16th 2010 at 02:19 AM.
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  2. #2
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    What you have to do is:

    1) Find either x as a function of y or y as a function of x. So manipulate one of the equations till you get x=... or y=...
    2) Substitute x or y in the OTHER equation and solve for the remaining variable. Now you have the value of either x or y.
    3) Fill in the value for your found x or y and you'll get your second value.

    Good luck!
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  3. #3
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    Those are 2 separate questions though. I don't know how to make 2 equations out of 1.
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  4. #4
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    Sorry my bad. Manipulate equation 1 to get x+\sqrt{y+2}=2+\sqrt{5}, now the answer lies in that x,y are both rational.
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  5. #5
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    Ohhh i see. Thanks (:
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  6. #6
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    The first equation can be written as

    x=2+\sqrt{5}-\sqrt{y+2}.

    You're told that x is rational, so there can't be a \sqrt{5} on the RHS because this is irrational. It has to be removed, and the only way to do this is to put y=3, leading then to x=2.

    The second equation can be solved using the same technique.
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