Question

已知:(a-b)((a^2+AB+b^2)/3-a^2b+ab^2=(a-b)^2​,且A不等于B,求A-B

Answer 1

(a-b)((a^2+AB+b^2)/3-a^2b+ab^2=(a-b)^2

即(a-b)(a²+ab+b²)/3 -a²b+ab²=(a-b)²

即(a-b)(a²+ab+b²)-3ab(a-b)=3(a-b)²

∵ a-b≠0

∴ a²+ab+b²-3ab=3(a-b)

即 a²+b²-2ab=3(a-b)

即 (a-b)²=3(a-b)

∵ a-b≠0

∴ a-b=3