Given that a and B are positive integers, the two real number roots of the equation x2-2ax + B = 0 for X are X1 and X2, and the two real number roots of the equation Y2 + 2ay + B = 0 for y are Y1 and Y2, and satisfy x1y1-x2y2 = 2008. Find the minimum value of B

Given that a and B are positive integers, the two real number roots of the equation x2-2ax + B = 0 for X are X1 and X2, and the two real number roots of the equation Y2 + 2ay + B = 0 for y are Y1 and Y2, and satisfy x1y1-x2y2 = 2008. Find the minimum value of B


Let A2 − B = t, then when X1 = a + T, X2 = A-T; Y1 = - A + T, y2 = - A-T, there is x1y1-x2y2 = 0, which does not satisfy the condition; when X1 = A-T, X2 = a + T; Y1 = - A-T, y2 = - A + T, there is x1y1 -