History of Hindu Mathematics: A Source Book v2.c17.s14.41

v2.c17.s14.41

In particular, taking α=α', β=β', and k=k', Brahmagupta finds from a solution x=α, y=β of the equation $Nx²+k=y²,$ a solution x=2αβ, y=β²+Nα² of the equation $Nx²+k²=y².$ That is, if $Nα²+k=β²,$ then $N(2αβ)²+k²=(β²+Nα²)². II$