History of Hindu Mathematics: A Source Book v2.c17.s17.t3.9

v2.c17.s17.t3.9

(i) Set x = my; so that equation (3) transforms into $z² = (am² + b) y² + c$ $= α y² + c,$ where α = am² + b. Hence the required solution of ax² + by² + c = z² is $x = my = m(rq ± ps),$ $y = rq ± ps,$ $z = sq ± α pr;$ where s² = α r² + c and q² = α p² + 1.