初中动脑竞赛题

a^3+b^3－3ab=1
不对，应该是a^3+b^3+3ab=1
=(a+b)(a^2-ab+b^2)+3ab
=1*(a^2-ab+b^2)+3ab
=a^2-ab+b^2+3ab
=a^2+2ab+b^2
=(a+b)^2
=1^2
1

a^2=a+1
两边平方
a^4=a^2+2a+1=(a+1)+2a+1)=3a+2
a^5=a^4*a=3a^2+2a=3(a+1)+2a=5a+1
a^5-5a+2
=5a+1-5a+2
=3

(a+b)^3=a^3+b^3+3a^2b+3ab^2=1
移项a3+b3=(a+b)^3-3a^2b-3ab^2
a3+b3－3ab
=(a+b)^3-3a^2b-3ab^2-3ab
=(a+b)^3-3ab(a+b)-3ab
己知a+b=1
原式=1-3ab-3ab=1 不成立
题目有错

a^2=a+1 平方
a^4=a^2+2a+1=(a+1)+2a+1)=3a+2
a^5=a^4*a=3a^2+2a=3(a+1)+2a=5a+1
a^5-5a+2=5a+1-5a+2=3