8-m/√(m-2)²+4√10=√5/5,m等于多少?
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将等式中所有的变量全部移项并平方，可以得到：
$$
\begin{aligned}
& 8 - \frac{m}{\sqrt{(m-2)^2 + 4\sqrt{10}}} = \frac{\sqrt{5}}{5} \\
\Rightarrow\ & \frac{m}{\sqrt{(m-2)^2 + 4\sqrt{10}}} = 8 - \frac{\sqrt{5}}{5} \\
\Rightarrow\ & \frac{m^2}{(m-2)^2+4\sqrt{10}} = \left(8 - \frac{\sqrt{5}}{5}\right)^2 \\
\Rightarrow\ & m^2 = (m-2)^2 + 4\sqrt{10}\left(8 - \frac{\sqrt{5}}{5}\right)^2 \\
\Rightarrow\ & m^2 = m^2 - 4m + 4 + 256\sqrt{10} - \frac{64\sqrt{10}}{5} + \frac{5}{5} \\
\Rightarrow\ & \frac{64}{5}\sqrt{10} - 4m = \frac{69}{5} \\
\Rightarrow\ & m = \frac{8\sqrt{10} - 69}{-20} \\
\Rightarrow\ & m \approx -0.364
\end{aligned}
$$
因此，方程的解为 $m \approx -0.364$。望采纳
$$
\begin{aligned}
& 8 - \frac{m}{\sqrt{(m-2)^2 + 4\sqrt{10}}} = \frac{\sqrt{5}}{5} \\
\Rightarrow\ & \frac{m}{\sqrt{(m-2)^2 + 4\sqrt{10}}} = 8 - \frac{\sqrt{5}}{5} \\
\Rightarrow\ & \frac{m^2}{(m-2)^2+4\sqrt{10}} = \left(8 - \frac{\sqrt{5}}{5}\right)^2 \\
\Rightarrow\ & m^2 = (m-2)^2 + 4\sqrt{10}\left(8 - \frac{\sqrt{5}}{5}\right)^2 \\
\Rightarrow\ & m^2 = m^2 - 4m + 4 + 256\sqrt{10} - \frac{64\sqrt{10}}{5} + \frac{5}{5} \\
\Rightarrow\ & \frac{64}{5}\sqrt{10} - 4m = \frac{69}{5} \\
\Rightarrow\ & m = \frac{8\sqrt{10} - 69}{-20} \\
\Rightarrow\ & m \approx -0.364
\end{aligned}
$$
因此，方程的解为 $m \approx -0.364$。望采纳
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