History of Hindu Mathematics: A Source Book v1.c8.s14.51

v1.c8.s14.51

¹ GSS, p. 54 (56). This problem is of the *aṁśa-mûla* variety, wherein fractional parts of square-roots are involved. The problems give equations of the form $x - a₁ √(b₁ x) - a₂ √(b₂ (x - a₁ √(b₁ x)))$ $- a₃ √(b₃ (x - a₁ √(b₁ x)) - a₂ √(b₂ (x - a₁ √(b₁ x)))) - = k.$ By repeated substitutions Mahâvîra reduces the equation to the form x - A√Bx - c = 0.