# Perfect Squares Only

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

• It has a real root $$d$$ 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 $$(a,b,c,d)$$, pick the one such that the discriminant is minimum. Find $$\sqrt{abcd}$$.

×