History of Hindu Mathematics: A Source Book v2.c17.s8.94

v2.c17.s8.94

*Solution.* "In this the value of the troop is *x*; its fifth part less three is ¹₅ x - 3; squared, ¹₂₅ x² - ⁶₅ x + 9; this added with the visible (number of monkeys), ¹₂₅ x² - ⁶₅ x + 10, is equal to the troop. Reducing to a common denominator, then deleting the denominator and making clearance, the two sides become $x² - 55x + 0 = 0x² + 0x - 250.$ Multiplying these by 4, adding the square of 55, and extracting roots, we get $2x - 55 = ± (0x + 45).$ In this case also, as in the previous, two values are obtained: 50, 5. But, in this case, the second (value) should not be accepted as it is inapplicable. *People have no faith in the known becoming negative.*"