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If $4 x^2-5 x y+y^2=0$ represents a pair of lines with slopes $m_1$ and $m_2$, then the value of $\left|m_1-m_2\right|$ equals
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The correct answer is:
3
Given, equation of lines
$$
4 x^2-5 x y+y^2=0 \Rightarrow y^2-5 x y+4 x^2=0
$$
Here,
$$
\text { re, } \begin{aligned}
m_1+m_2 & =5 \\
m_1 m_2 & =4 \\
\left(m_1-m_2\right)^2 & =\left(m_1+m_2\right)^2-4 m_1 m_2 \\
\left(m_1-m_2\right)^2 & =(5)^2-4(4) \\
\left|m_1-m_2\right| & =\sqrt{25-16}=3
\end{aligned}
$$
$$
4 x^2-5 x y+y^2=0 \Rightarrow y^2-5 x y+4 x^2=0
$$
Here,
$$
\text { re, } \begin{aligned}
m_1+m_2 & =5 \\
m_1 m_2 & =4 \\
\left(m_1-m_2\right)^2 & =\left(m_1+m_2\right)^2-4 m_1 m_2 \\
\left(m_1-m_2\right)^2 & =(5)^2-4(4) \\
\left|m_1-m_2\right| & =\sqrt{25-16}=3
\end{aligned}
$$
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