If p and q are the roots of the equation x2 ?15x + r = 0 and p ?q = 1, then what is the value of r ?

In the below equation,

x2?15x + r = 0

sum of roots = p + q = -(-15)/1 = 15 (sum of roots for equation ax2+ bx + c is -b/a)

product of roots = pq = r/1 = r     (product of roots for equation ax2+ bx + c is c/a)

given p ?q = 1

also we know that p+q = 15

subtracting the squares of both

(p+q)2 + (p-q)2 = 15^2?1

p2 + q2 + 2pq ?p2 ?q2 +2pq = 225 -1

4pq = 224

4r = 224

r = 56