问题补充:
a^3/(a-b)(a-c)+b^3/(b-c)(b-a)+c^3/(c-a)(c-b) =a+b+c 证明
答案:
通分即可[a^3(b-c)+b^3(a-c)+c^3(a-b)]/(a-b)(a-c)(b-c)
=[a^3b-a^3c+b^3a-b^3c+c^3a-c^3b](a-b)(a-c)(b-c)
=(a+b+c)(a-b)(a-c)(b-c)/(a-b)(a-c)(b-c)
=a+b+c
时间:2022-05-04 23:02:12
a^3/(a-b)(a-c)+b^3/(b-c)(b-a)+c^3/(c-a)(c-b) =a+b+c 证明
通分即可[a^3(b-c)+b^3(a-c)+c^3(a-b)]/(a-b)(a-c)(b-c)
=[a^3b-a^3c+b^3a-b^3c+c^3a-c^3b](a-b)(a-c)(b-c)
=(a+b+c)(a-b)(a-c)(b-c)/(a-b)(a-c)(b-c)
=a+b+c