\(\Delta=m^2-4\left(-8\right)=m^2+32>0\left(\forall m\right)\)
\(\Rightarrow pt\) \(luôn\) \(có\) \(2ng\) \(phân\) \(biệt\)
\(\left\{{}\begin{matrix}x1+x2=m\\x1x2=8\end{matrix}\right.\) \(do;x1;x2\) \(là\) \(nghiệm\Rightarrow\left\{{}\begin{matrix}x1^2-mx1-8=0\Leftrightarrow x1^2=mx1+8\\x2^2-mx2-8=0\Leftrightarrow x2^2=mx2+8\end{matrix}\right.\)
\(H=\dfrac{2\left(mx1+8\right)+5x1-16}{3x1}=\dfrac{2\left(mx2+8\right)+5x2-16}{3x2}\Leftrightarrow\dfrac{x1\left(2m+5\right)}{3x1}=\dfrac{x2\left(2m+5\right)}{3x2}\Leftrightarrow\dfrac{2m+5}{3}=\dfrac{2m+5}{3}\Leftrightarrow0=0\left(đpcm\right)\)
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