請找出xy的值

(x + 22)/y + 290/xy = (26 - y) / x , where, x ≠ 0 and y ≠ 0
x(x + 22) + 290 = y(26 - y)
x^2 + 22x + 290 + y^2 - 26y = 0
(x + 11)^2 - 121 + 290 + y^2 - 26y = 0
(x + 11)^2 + y^2 - 26y + 169 = 0
(x + 11)^2 + (y - 13)^2 = 0
Since x and y are real numbers,
(x + 11)^2 = 0 and (y - 13)^2 = 0
x = -11 and y = 13
i.e. xy = (-11)(13) = -143