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    Hi there, could somebody help me solve this equation?
    \sqrt{t} = 4 + \frac{12}{\sqrt{t}}
    Thanks
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    Multiply through by \sqrt{t}. If it helps, make the substitution u=\sqrt{t} -- it's a quadratic in disguise.
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    Ok so this is what I have so far, but I still don't really understand how to solve it.

    U = \sqrt{t}

    U = 4 + \frac{12}{U}

    Could somebody tell me what to do next?
    Thanks
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    (Original post by vivaespana)
    Ok so this is what I have so far, but I still don't really understand how to solve it.

    U = \sqrt{t}

    U = 4 + \frac{12}{U}

    Could somebody tell me what to do next?
    Thanks
    U^2 = 4U + 12
    U^2-4U-12 = 0
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    (Original post by vivaespana)
    Ok so this is what I have so far, but I still don't really understand how to solve it.

    U = \sqrt{t}

    U = 4 + \frac{12}{U}

    Could somebody tell me what to do next?
    Thanks
    Multiply both sides by U as nuodai said. So you get:
    U^2 = U(4+\frac{12}{U})
    Expand out the RHS, collect all terms on one side and solve the quadratic. Then note that U=\sqrt t, so set your solutions for U equal to \sqrt t and solve for t. REMEMBER, \sqrt t CANNOT BE NEGATIVE (assuming t is real, which I'm guessing it is judging by the difficulty of the question).
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    (Original post by IAmTheChosenOne)
    U^2 = 4U + 12
    U^2-4U-12 = 0
    factorise this to get (u + 2)(u - 6) = 0, so u = -2 or u = 6?
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    multiply through so you get U^2 = 4U + 12
    then U^2 - 4U -12 = 0
    then (U -6)(U + 2) = 0
    so U = 6, or U = -2
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    (Original post by vivaespana)
    Ok so this is what I have so far, but I still don't really understand how to solve it.

    U = \sqrt{t}

    U = 4 + \frac{12}{U}

    Could somebody tell me what to do next?
    Thanks
    Multiply by U to get a quadratic.

    Put in the form ax^2 + bx + c = 0.

    Solve by factorisation.

    U = root (t)

    Find t by squaring both sides.

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    Thanks guys I understand it now
 
 
 
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Updated: September 25, 2010
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