History of Hindu Mathematics: A Source Book v2.c17.s23.60

v2.c17.s23.60

*Example* with solution from Bhâskara II:¹ .2(x² - y²) + 3 = u² / 3(x² - y²) + 3 = v²}. Set x² - y² = z; then 2z + 3 = u², / 3z + 3 = v². Eliminating z we get 3u² = 2v² + 3, or (3u)² = 6v² + 9. Whence v = 6, 60, 3u = 15, 147, \dots Therefore u = 5, 49, Hence x² - y² = z = 11, 1199,