The product of all the rational roots of the equation $\left(x^2 - 9x + 11\right)^2 - (x-4)(x-5) = 3$, is equal to
(1) 14
(2) 21
(3) 28
(4) 7

2. For ALL APPLICANTS.

Suppose that the equation
$$x ^ { 4 } + A x ^ { 2 } + B = \left( x ^ { 2 } + a x + b \right) \left( x ^ { 2 } - a x + b \right)$$
holds for all values of $x$.
(i) Find $A$ and $B$ in terms of $a$ and $b$.
(ii) Use this information to find a factorization of the expression
$$x ^ { 4 } - 20 x ^ { 2 } + 16$$
as a product of two quadratics in $x$.
(iii) Show that the four solutions of the equation
$$x ^ { 4 } - 20 x ^ { 2 } + 16 = 0$$
can be written as $\pm \sqrt { 7 } \pm \sqrt { 3 }$.

Let x and y be real numbers such that
$$\begin{aligned} & x ^ { 3 } - 3 x ^ { 2 } y = 3 \\ & y ^ { 3 } - 3 x y ^ { 2 } = 11 \end{aligned}$$
Accordingly, what is the difference $x - y$?
A) 3
B) 2
C) 1
D) - 2
E) - 3