Perfect Squares Only

Let a,b,ca,b,c be nonzero perfect squares such that b=a+cb = a+c. The equation ax2bx+c=0ax^2 - bx + c = 0 has the following properties:

  • It has a real root dd that is greater than 1. (The other root may or may not be real.)
  • The square root of the quadratic discriminant is a prime number.

Among all such (a,b,c,d)(a,b,c,d), pick the one such that the discriminant is minimum. Find abcd\sqrt{abcd}.

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