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Answer:
Method 1:
x^2+(1991+a)x+1991a+1
Now for integers d should be either 0 or perfect square so,
(1991+a)^2-4*1991a-4
(1991-a)^2-4
(1989-a)(1993-a)
They both can be equal so for d = 0
a = 1989, a = 1993
Method 2:
b and c are roots
(-b+a) (-b+1991) +1 = 0
(-b+a) (-b+1991) = -1*1
a-b = -1 and 1991 - b = 1
or
a-b=1 and 1991-b = -1
2 values of a and b
a = 1989 and 1993 Sum = 3982.
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