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Math Help - Equation

  1. #1
    Member jacs's Avatar
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    Equation

    hi, i can't sort out what to do with this one:

    <br />
\sqrt{2m-3}=\sqrt{m+7} - 2<br />


    thanks

    jacs
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  2. #2
    Senior Member OReilly's Avatar
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    \begin{array}{l}<br />
 \sqrt {2m - 3}  = \sqrt {m + 7}  - 2 \\ <br />
 \left( {\sqrt {2m - 3} } \right)^2  = \left( {\sqrt {m + 7}  - 2} \right)^2  \\ <br />
 2m - 3 = m + 7 - 4\sqrt {m + 7}  + 4 \\ <br />
 2m - 3 - m - 7 - 4 =  - 4\sqrt {m + 7}  \\ <br />
 \end{array}<br />
    \begin{array}{l}<br />
 m - 14 =  - 4\sqrt {m + 7}  \\ <br />
 \left( {m - 14} \right)^2  = \left( {4\sqrt {m + 7} } \right)^2  \\ <br />
 m^2  - 28m + 196 = 16(m + 7) \\ <br />
 m^2  - 28m + 196 - 16m - 112 = 0 \\ <br />
 m^2  - 44m + 84 = 0 \\ <br />
 \end{array}<br />
    m_{1/2}  = \frac{{44 \pm \sqrt {1936 - 336} }}{2} = \frac{{44 \pm \sqrt {1600} }}{2} = \frac{{44 \pm 40}}{2}
    m_1  = 42 \wedge m_2  = 2

    Solution is m=2.
    Last edited by OReilly; April 9th 2006 at 06:43 AM.
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  3. #3
    Member jacs's Avatar
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    thanks OReilly, i see it now. I got half way and then didnt know how to proceed, but it is just manipulating them cleverly.

    thanks,for that

    i appreciate it

    jacs
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