$$\begin{aligned} &\left(x^2-9 x+11\right)^2-\left(x^2-9 x+20\right)=3\\ &\text { Let }\\ &\begin{aligned} & \Rightarrow \mathrm{x}^2-9 \mathrm{x}=\mathrm{t} \\ & \Rightarrow \mathrm{t}^2+22 \mathrm{t}+121-\mathrm{t}-20-3=0 \\ & \Rightarrow \mathrm{t}^2+21 \mathrm{t}+98=0 \\ & \Rightarrow(\mathrm{t}+14)(\mathrm{t}+7)=0 \\ & \Rightarrow \mathrm{t}=-7,-14 \end{aligned} \end{aligned}$$

$$\begin{aligned} &\text { So, }\\ &\begin{aligned} & x^2-9 x=-7,-14 \\ & x^2-9 x+7=0 \quad \text { or } \quad x^2-9 x+14=0 \end{aligned} \end{aligned}$$

$$\begin{aligned} &\begin{array}{ll} x=\frac{9 \pm \sqrt{81-4(7)}}{2 \times 1} & x=\frac{9 \pm \sqrt{81-4(14)}}{2} \\ =\frac{9 \pm \sqrt{53}}{2} & =\frac{9 \pm 5}{2} \end{array}\\ &\text { Product of all rational roots }=7 \times 2=14 \end{aligned}$$