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Homework Help: 3(x)^1/2 = (x)^1/2 help

  1. Jul 3, 2005 #1
    3(x)^1/2 = (x)^1/2

    How come there are two answers for this equation?? 0 and 1/3
  2. jcsd
  3. Jul 3, 2005 #2


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    Your equation is
    [tex] 3 \sqrt{x} = \sqrt {x} [/tex]

    How is 1/3 a solution?
    On substituting 1/3 in the Left Hand side you get [tex]\sqrt 3 [/tex]

    On substituting 1/3 in the Right Hand side you get [tex] \frac {1}{\sqrt 3} [/tex]

    So LHS is not equal to RHS.
    This means that 1/3 is not a solution
  4. Jul 3, 2005 #3
    You should first square each side to get rid of the square root, giving you:

    9x = x

    And x = 0 should be your only answer
  5. Jul 3, 2005 #4


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    [tex]3 \sqrt{x} = \sqrt{x}[/tex]

    [tex]3 \sqrt{x} - \sqrt{x} = 0[/tex]

    [tex]2 \sqrt{x} = 0[/tex]

    [tex]\sqrt{x} = 0[/tex]

    I think there is only one solution to that.
  6. Jul 3, 2005 #5
    You don't need to. It should be clear that x = 0, otherwise you'd have 3 = 1.
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