Question

a的三次方-b的三次方=3a的二次方b-3ab的二次方+1，其中a，b为实数，则a-b=

Answer 1

解：
a³-b³ = 3a²b-3ab²+1
a³-3a²b+3ab²-b³ = 1
(a-b)³ = 1
∴ a-b = 1

Answer 2

a^3-b^3=3a^2b-3ab^2+1
(a-b)(a^2+b^2+ab)=3ab(a-b)+1
(a-b)(a^2+b^2+ab)-3ab(a-b)=1
(a-b)(a^2+b^2-2ab)=1
(a-b)(a-b)^2=1
(a-b)^3=1
a-b=1