令 (a - b)(b - c)(c - a) = k ≠ 0
則 (c + a)/(c - a) = -90/k
c/a = (90 - k)/(90 + k)
同理 c/b = (42 - k)/(42 + k),a/b = (60 - k)/(60 + k)
[(90 - k)/(90 + k)][(60 - k)/(60 + k)] = (42 - k)/(42 + k)
k = -30 or 30 or 0(不合)
k = -30,c = 2a = 6b
a = 3,b = 1,c = 6
k = 30,b = 3a = 6c
a = 12^(1/3),b = 324^(1/3),c = (3/2)^(1/3)