hi, i can't sort out what to do with this one:
$\displaystyle
\sqrt{2m-3}=\sqrt{m+7} - 2
$
thanks
jacs
$\displaystyle \begin{array}{l}
\sqrt {2m - 3} = \sqrt {m + 7} - 2 \\
\left( {\sqrt {2m - 3} } \right)^2 = \left( {\sqrt {m + 7} - 2} \right)^2 \\
2m - 3 = m + 7 - 4\sqrt {m + 7} + 4 \\
2m - 3 - m - 7 - 4 = - 4\sqrt {m + 7} \\
\end{array}
$
$\displaystyle \begin{array}{l}
m - 14 = - 4\sqrt {m + 7} \\
\left( {m - 14} \right)^2 = \left( {4\sqrt {m + 7} } \right)^2 \\
m^2 - 28m + 196 = 16(m + 7) \\
m^2 - 28m + 196 - 16m - 112 = 0 \\
m^2 - 44m + 84 = 0 \\
\end{array}
$
$\displaystyle m_{1/2} = \frac{{44 \pm \sqrt {1936 - 336} }}{2} = \frac{{44 \pm \sqrt {1600} }}{2} = \frac{{44 \pm 40}}{2}$
$\displaystyle m_1 = 42 \wedge m_2 = 2$
Solution is $\displaystyle m=2$.