History of Hindu Mathematics: A Source Book v2.c17.s17.t3.12

v2.c17.s17.t3.12

If z = s, w = r be a solution of this equation, another solution will be $z = sq ± rp,$ $w = rq ± α sp;$ where q² = α p² + 1. Hence the solution of ax² + by² + c = z² is $x = m/(α) (rq ± α sp amn) ± n,$ $y = 1/(α) (rq ± α sp amn),$ $z = sq ± rp;$ where q² = α p² + 1, r² = α s² - β, α = am² + b and β = a(bn² + cm²) + bc.