History of Hindu Mathematics: A Source Book v2.c17.s10.62

v2.c17.s10.62

**Mahâvîra's Rules.** Mahâvîra (850) has treated certain problems involving the simultaneous quadratic equations : $u + x = a, & urw = α x, / u + y = b. & usw = α y.$ $Here r/s = x/y = (a - u)/(b - u).$ $Therefore u = (rb - sa)/(r - s).$ $Hence x = ((a - b)/(r - s))r, y = ((a - b)/(r - s))s, w = ((a - b)/(rb - sa))α.$