設a³-b³=485,a-b=5,則ab=?

已知 a - b = 5
(a - b)² = 25
a² - 2ab + b² = 25
a² + b² = 25 + 2ab

考慮
a³ - b³ = (a - b)(a² + ab + b²)
485 = 5(25 + 2ab + ab)
485 = 5(25 + 3ab)
97 = 25 + 3ab
3ab = 72
ab = 24

a-b=5
(a-b)^3=125
a^3-3(a^2)b+3ab^2+b^3=125
485-3(a^2)b+3ab^2=125
3ab(-a+b)=-360
-ab(a-b)=-120
5ab=120
ab=24