回復 1# stevetain 的帖子
第1題
\(\displaystyle\begin{align}
& \frac{{{x}^{2}}}{7{{x}^{2}}-4x+1}=k \\
& \left( 7k-1 \right){{x}^{2}}-4kx+k=0 \\
& {{\left( -4k \right)}^{2}}-4k\left( 7k-1 \right)\ge 0 \\
& 0\le k\le \frac{1}{3} \\
\end{align}\)
第2題
\(\displaystyle \begin{align}
& {{\left[ -2\left( 2m-5 \right) \right]}^{2}}-4\left( 3{{m}^{2}}-16m+{{k}^{2}}+5k \right) \\
& =4\left[ {{m}^{2}}-4m-\left( {{k}^{2}}+5k-25 \right) \right] \\
& =4\left[ {{\left( m-2 \right)}^{2}}-\left( {{k}^{2}}+5k-21 \right) \right] \\
\end{align}\)
是完全平方數
\({{k}^{2}}+5k-21=0\)
