History of Hindu Mathematics: A Source Book v2.c17.s8.92

v2.c17.s8.92

*Solution.* "Here the troop of monkeys is *x*. The square of the eighth part of this together with 12, is equal to the troop. So the two sides are¹ $¹₆₄x² + 0x + 12 = 0x² + x + 0.$ Reducing these to a common denominator and then deleting the denominator, and also making clearance, the two sides become $x² - 64x + 0 = 0x² + 0x - 768.$ Adding the square of 32 to both sides and (extracting) square-roots, we get $x - 32 = ± (0x + 16).$ In this instance the absolute term on the known side is smaller than the negative absolute term on the side of the unknown; hence it is taken positive as well as negative; the two values of *x* are found to be 48, 16."