Perfect Squares Only
Number Theory
Level
5
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 \(\sqrt{abcd}\).
by
Worranat Pakornrat