The number of positive integral solutions of ⁻¹ x+ ⁻¹ ( y 1+y^2 )= ⁻¹ ( 3 10 ) are

Step-by-step solution

The equation is ⁻¹ x + ⁻¹ ( y 1+y^2 ) = ⁻¹ ( 3 10 ) . Since y > 0 , we have ⁻¹ ( y 1+y^2 ) = ⁻¹ ( 1 y ) by constructing a right triangle with opposite side 1 and adjacent side y . Similarly, ⁻¹ ( 3 10 ) = ⁻¹(3) with adjacent side 1 and opposite side 3 . Substituting yields ⁻¹ x + ⁻¹ ( 1 y ) = ⁻¹(3) . For x The positive integer solutions satisfying y + 3 4 and x - 3 -2 are (y + 3, x - 3) = (5, -2) giving (y, x) = (2, 1) and (10, -1) giving (y, x) = (7, 2) . Both satisfy x For x = y , ⁻¹ x + ⁻¹ ( 1 x ) = 2 ⁻¹(3) , yi