題設：【x和y是兩個絕對值不同的實數】

故x不會等於-y，即0不是答案。只有133。

0 或133

x^3 = 13x + 3y (1)

y^3 = 3x + 13y (2)

(1) + (2):

(x+y) (x^2-xy + y^2) = 16 (x+y)

x = -y, or (3)

x^2-xy + y^2 = 16 (4)

(1) – (2):

(x-y) (x^2 + xy + y^2) = 10 (x-y)

x = y, or (5)

x^2 + xy + y^2 = 10 (6)

從 (4) 和 (6),

x^2 + y^2 = 13 (7)

xy = -3 (8)

從 (3) 和 (4),

(x^2 - y^2)^2 = 0

從 (7) 和 (8),

(x^2 - y^2)^2 = x^4 + y^4 -2x^2*y^2 = (x^2 + y^2)^2 -4*(xy)^2 = 13^2 -4*3^2 = 133