History of Hindu Mathematics: A Source Book v2.c17.s22.42

v2.c17.s22.42

Now, a rational solution of the equation abp² + 1 = q² is p = 2t/(t² - ab), q = (t² + ab)/(t² - ab), where t is any rational number. Therefore, the above general solution becomes .x &= 1/(a(t² - ab)²)l{ r(t² + ab) ± 2st r}² - c/a, / u &= 1/((t² - ab))l{ r(t² + ab) ± 2st r}, / v &= 1/(a(t² - ab))l{ s(t² + ab) ± 2abrt r}, } (1.3) where abr² + a²d - abc = s².