Let A and B be two matrices such that A=[aij]=⎡⎢⎣x123x−114x2+1⎤⎥⎦ and B=[bij]=⎡⎢⎢⎢⎣1x21x2x23x⎤⎥⎥⎥⎦, where x>0. If C=[cij]=AB and the minimum value of Δ(x)=∑i≤i≤j≤2cij is pq, where p and q are co-prime numbers, then the value of p+q is

Let A and B be two matrices such that A=[aij]=⎡⎢⎣x123x−114x2+1

1.	Let A and B be two matrices such that A=[aij]=⎡⎢⎣x123x−114x2+1⎤⎥⎦ and B=[bij]=⎡⎢⎢⎢⎣1x21x2x23x⎤⎥⎥⎥⎦, where x>0. If C=[cij]=AB and the minimum value of Δ(x)=∑i≤i≤j≤2cij is pq, where p and q are co-prime numbers, then the value of p+q is
Answer» Let $A$ and $B$ be two matrices such that $A = [a_{i j}] = ⎡ ⎢ ⎣ \begin{matrix} x & 1 & 2 3 x & - 1 & \frac{1}{4 x^{2} + 1} \end{matrix} ⎤ ⎥ ⎦$ and $B = [b_{i j}] = ⎡ ⎢⎢⎢ ⎣ \begin{matrix} \frac{1}{x^{2}} & \frac{1}{x} 2 x & 2 3 & x \end{matrix} ⎤ ⎥⎥⎥ ⎦$ , where $x > 0$ . If $C = [c_{i j}] = A B$ and the minimum value of $Δ (x) = \sum i \leq i \leq j \leq 2 c_{i j}$ is $\frac{p}{q}$ , where $p$ and $q$ are co-prime numbers, then the value of $p + q$ is