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Math Help - inequality 4

  1. #1
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    inequality 4

    How do you solve a problem like this by taking the square of boyh sides?

    x+2>square root of x^2-16

    Answer is : x>=4.Square root can't be-.But there is not a method to solve this one.
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  2. #2
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    Re: inequality 4

    first check domain on both sides for sqrt(x^2-16) it is (-infinity to -4]U[4,infinity)
    and for x+2 it is any real no
    now sqrt(x^2-16)>=0
    so x+2 takes positive values
    so it can have domain as [0,infinity)
    but we need to take in consideration the right hand side which contains square root term
    if we split [0,infinity) into two parts i.e.
    [0,4)U[4,infinity)
    we see that [0,4) does not satisfy the domain for right hand side
    so x belongs to [4,infinity)
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  3. #3
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    Re: inequality 4

    thanks.
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