History of Hindu Mathematics: A Source Book v2.c17.s22.11

v2.c17.s22.11

The *rationale* is very simple. Since $u² = x ± a, v² = x ± b,$ we have $u² - v² = ± a b.$ Therefore $u - v = m,$ and $u + v = (± a b)/m,$ where m is arbitrary. Hence $u = ½ ( (± a b)/m + m ) = ± ½ ( (a - b)/m ± m ).$