History of Hindu Mathematics: A Source Book v2.c17.s24.34

v2.c17.s24.34

*Second Method.* Assume x = 2w², y = 7w². Then $x + y = 9w² = (3w)².$ So the equation (2) is satisfied. Now, substituting those values in (1) we get $8w⁶ + 49w⁴ = u²,$ or $w⁴(8w² + 49) = u².$ If $8w² + 49 = z²,$ then $u = zw².$ Now the values of w making 8w² + 49 a square are 2, 3, 7 Hence the required numbers (x, y) are (8, 28), (18, 63), (98, 343),