History of Hindu Mathematics: A Source Book v2.c17.s21.36

v2.c17.s21.36

We take the following illustrative example with its solution from Bhâskara II :¹ 5y² + 3 = 16x. Multiplying by 5, and putting u = 5y, v = 5x, we get u² = 16v - 15. The solution of this is u = 8w ± 1, v = 4w² ± w + 1. Therefore, we have (1) 5y &= 8w + 1, / or (2) 5y &= 8w - 1. Now, solving by the method of the pulveriser, we get the solution of (1) as y = 8t + 5, w = 5t + 3; and that of (2) as y = 8t + 3, w = 5t + 2; where *t* is any rational number.