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Algebra and square root simplification

  1. Feb 14, 2014 #1
    1. The problem statement, all variables and given/known data

    Points A and B are 10 km apart and it is determined from the sound of an explosion heard at those points at different times that the location of the explosion is 6 km closer to A than B. Show that the location of the explosion is restricted to a particular curve and find an equation of it.

    2. Relevant equations
    √((x − 5)2 + y2) - √((x + 5)2 + y2) = 6


    3. The attempt at a solution

    i must simplify this to get x2/9 - y2/16 = 1

    it is a hyperbola i guess

    i applied (a-b)^2 = a^2 -2ab +b^2

    if i square both sides i am still getting square root because 2ab is twice the product of 1st and 2nd roots which is again a root

    if i square both sides again i still get a root

    if i bring one root to the other side and square both sides still i am getting a root

    how do i cancel the roots
     
    Last edited: Feb 15, 2014
  2. jcsd
  3. Feb 14, 2014 #2

    haruspex

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    (For the purposes of the template, this is part of the problem statement, not a 'relevant equation'.)
    I presume you mean √((x − 5)2 + y2) + √((x + 5)2 + y2) = 6
    After squaring both sides there will only be one square root term. Isolate that on one side of the equation and square again.
     
  4. Feb 14, 2014 #3
    if i do that the result i am getting is
    x4 + 51x2 + 52y2x2 + y2 + y4 + 632 = 0

    which is not a hyperbola i guess
     
  5. Feb 14, 2014 #4

    haruspex

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    Funny, I didn't notice the problem statement before - only saw the equation you posted. Did you add the problem statement in an edit? I may have had a stale window.
    So actually the equation should be in the attempt at solution section.
    Anyway, it is wrong. Think about the signs.
     
  6. Feb 14, 2014 #5

    LCKurtz

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    It isn't anything, since the left side is positive and the right side is zero.
     
  7. Feb 15, 2014 #6
    yes i did

    i changed the signs,instead of + it must be -
    but still the result i am getting is x^4 + 51x^2 + 52y^2 x^2 + y^2 + y^4 + 632 = 0
     
  8. Feb 15, 2014 #7

    haruspex

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    Then you've made a mistake in the algebra. Starting from
    √((x − 5)2 + y2) - √((x + 5)2 + y2) = 6
    all the x4, y4 and x2y2 terms should cancel.
    If still stuck, please post all your working.
     
  9. Feb 15, 2014 #8

    Mark44

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    The original equation in post #1 was edited, and is now as follows:
    This looks fine to me.

    1. Moved one of the radicals to the other side and then square both sides.
    2. Simplify the resulting equation. (Many terms drop out.)
    3. Leave the radical where it is, and move the other terms to the other side.
    4. Square both sides again.

    The resulting equation is what you want.
     
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