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Confused with the answer<> seems correct buttht's wrong wrong?

  1. Mar 4, 2012 #1
    confused with the answer<> seems correct buttht's wrong wrong???????

    question is
    sqrt(x+1)-sqrt(x-1)=sqrt(4x-1) - - - - - - - - - - - - - - - - - - - - - - - (1)
    squaring both sides
    (x+1)+(x-1)-2*sqrt(x2-1)=4x-1 - - - - - - - - - - - - - - - - (2)
    solving and rearranging
    1-2x=2*sqrt(x2-1) - - - - - - - - - - - - - - - - - - - - - - - -(3)
    once again squaring both sides;
    1-4x= -4
    x=5/4;
    But it does not satisfy the first equation.
    it also doesn't satisfying equation number three, Is it reason for this????
    If yes then why it is so?>?>?>?>?>?>(this is my question)
     
  2. jcsd
  3. Mar 4, 2012 #2

    jamesrc

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    Re: confused with the answer<> seems correct buttht's wrong wrong???????

    Are you sure that your solution doesn't satisfy those equations? When you take the square root of a number, how many solutions do you get?
     
  4. Mar 4, 2012 #3

    Fredrik

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    Re: confused with the answer<> seems correct buttht's wrong wrong???????

    You seem to have started with an equation that doesn't have any real solutions. Let's consider a simpler problem: Find all real numbers x such that ##\sqrt x =-1##. If you square both sides, you get x=1. But x=1 doesn't satisfy the original equation, since ##\sqrt 1=1\neq -1##.

    By squaring both sides, we only proved that if ##\sqrt x=-1##, then ##x=1##. This is an implication, not an equivalence, since x=1 doesn't imply ##\sqrt x=-1##. So we can't conclude that x=1. We can only conclude that there are no solutions with x≠1.
     
  5. Mar 4, 2012 #4

    Mark44

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    Re: confused with the answer<> seems correct buttht's wrong wrong???????

    I'm not sure where you're going with this question.

    When you take the square root of a number, you get one value. Were you going to suggest that there are two?
     
  6. Mar 4, 2012 #5

    mathman

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    Re: confused with the answer<> seems correct buttht's wrong wrong???????

    Equation (3) lhs = -3/2, rhs = 3/2, so the squares are =, which is the source of your problem.
     
  7. Mar 4, 2012 #6
    Re: confused with the answer<> seems correct buttht's wrong wrong???????

    thanks to all of you;
    i have got the point of error.
    squaring add some extra answers to our solutions.....
     
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