The product of all the rational roots of the equation (x² – 9x + 11)² – (x – 4) (x – 5) = 3, is equal to :  

$\begin{array}{l}{\left({\mathrm{x}}^2-9\mathrm{x}+11\right)}^2-\left({\mathrm{x}}^2-9\mathrm{x}+20\right)=3\\ \text{ Let }\\ \begin{array}{rl} & \Rightarrow {\mathrm{x}}^2-9\mathrm{x}=\mathrm{t}\\ & \Rightarrow {\mathrm{t}}^2+22\mathrm{t}+121-\mathrm{t}-20-3=0\\ & \Rightarrow {\mathrm{t}}^2+21\mathrm{t}+98=0\\ & \Rightarrow (\mathrm{t}+14)(\mathrm{t}+7)=0\\ & \Rightarrow \mathrm{t}=-7,-14\end{array}\end{array}$
So, ${\mathrm{x}}^2-9\mathrm{x}=-7,-14$
$\begin{array}{l}{\mathrm{x}}^2-9\mathrm{x}+7=0\text{ or }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{\mathrm{x}}^2-9\mathrm{x}+14=0\\ \mathrm{x}=\frac{9\pm \sqrt{81-4\left(7\right)}}{2\times 1}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{x}=\frac{9\pm \sqrt{81-4\left(14\right)}}{2}\\ =\frac{9\pm \sqrt{53}}{2}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}=\frac{9\pm 5}{2}\end{array}$
Product of all rational roots = 7 × 2 = 14