History of Hindu Mathematics: A Source Book v2.c17.s23.69

v2.c17.s23.69

Bhâskara II gives the following illustrative example together with its solution:¹ .x² + xy + y² &= u² / (x + y)u + 1 &= v²}. Multiplying the first equation by 36, we get (6x + 3y)² + 27y² = 36u². Whence 6x + 3y &= 1/2l((27y²)/(\lambda) - \lambdar), / 6u &= 1/2l((27y²)/(\lambda) + \lambdar), where λ is an arbitrary rational number. Taking λ = y, we have 6x + 3y &= 13y, / x &= 5/3y, / u &= 7/3y. Substituting in the second equation, we get 56y² + 9 = 9v². By the method of the Square-nature the values of y are 6, 180, ...