History of Hindu Mathematics: A Source Book v2.c17.s20.16

v2.c17.s20.16

If x, y be the numbers, then by the statement of the question $(x + y)² + (x + y)³ = 2(x³ + y³).$ "Here, so that the operations may not become lengthy," says Bhâskara II, "assume the two numbers to be u + v and u - v." So on putting $x = u + v, y = u - v,$ the equation reduces to $4u³ + 4u² = 12uv²,$ or 4u² + 4u = 12v², or (2u + 1)² = 12v² + 1.