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Homework Help: Extracting a square root

  1. Jan 31, 2010 #1
    1. The problem statement, all variables and given/known data

    (x-7)^2=(x+3)^2

    2. The attempt at a solution

    I squared both sides and received x-7=x+3

    However, that cannot be correct because the variables cancel out which means there is no solution. The book shows that there is a solution of 2
     
  2. jcsd
  3. Jan 31, 2010 #2
    hi, instead of squaring both sides, try multiplying them out as you know (x-7)^2 is the same as (x-7)(x-7) ..
     
  4. Jan 31, 2010 #3

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You mean you took the square root of both sides?

    Well, there's a problem: the phrase
    a2 is the square of b​
    is not synonymous with
    a is b​

    So you cannot infer that the two square roots are equal....
     
  5. Jan 31, 2010 #4

    Mark44

    Staff: Mentor

    Supplementing what Hurkyl said, if a2 = b2, then a = +/b. You can apply this principle to your equation.
     
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