Question

Let p and q are distinct naturals such that 2005+p=q² and 2005+q=p².Find the value of 2014+pq

Answer 1

(2005+p)-(2005+q)=q^2-p^2

p-q=(q-p)(p+q)

p+q=(-1)

p^2+q^2=p+q+4010=4009

(p+q)^2=p^2+q^2+2pq=1

4009+2pq=1

pq=(-2004)

2014+pq=2014-2004=10