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Let the angle between the lines $x-2 y+3=0$ and $k x-y+2=0$ be $45^{\circ}$. If $k_1, k_2\left(k_1>k_2\right)$ are two distinct real values of $k$, then $k_1-2=$
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$-3 \mathrm{k}_2$
$\begin{aligned} & \text {} \tan 45^{\circ}=\left|\frac{\frac{1}{2}-k}{1+\frac{k}{2}}\right| \\ & \Rightarrow \quad\left|\frac{1}{2}-k\right|=\left|1+\frac{k}{2}\right| \\ & \Rightarrow \quad|1-2 k|=|2+k| \\ & \therefore \quad 1-2 k= \pm(k+2) \\ & \quad 1-2 k=k+2 \text { or } 1-2 k=-(k+2) \\ & 3 k=-1 \text { or } 1-2 k=-k-2 \\ & \quad k=\frac{-1}{3} \text { or } k=3 \\ & \therefore \quad k_1=3, k_2=\frac{-1}{3} \\ & k_1-2=1=-3 k_2 .\end{aligned}$
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