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Solving for X involving Square Roots

  1. Mar 4, 2008 #1
    Hi, I am getting frustrated with trying to solve this equation:

    sqrt(x+9) - sqrt(x-6) = 3.

    I know that the answer is x=7 because of guess and check. I don't know how to show it algebraically. Squaring both sides will cancel out the x. Is there a trick or something this? Please help. Thanks in advance.
  2. jcsd
  3. Mar 4, 2008 #2
    Can you show how squaring both sides cancels out the x?

    If I square both sides I get:

    (sqrt(x+9) - sqrt (x-6))^2 = 3^2

    x+9 - 2*sqrt(x+9)*sqrt(x-6) + x - 6 = 9

    2x + 3 - 2*sqrt((x+9)(x-6)) = 9
  4. Mar 4, 2008 #3
    oh i see what you are saying. Silly mistake on me. Thank you so much!
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