Question

a+b=1,ab=-1,a5次方+b5次方

Answer 1

a平方+b平方=1X1-2X（-1）=3
a平方b平方=1
a3次方+b3次方=（a平方+b平方）X（a+b）-ab（a+b）=3X1-1X（-1）=5
同理a4次方+b4次方=5X1-3X（-1）=8
同理所以a5次方+b5次方=8X1-5X（-1）=13

Answer 2

a^5+b^5
=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)
=a^4-a^3b+a^2b^2-ab^3+b^4
=(a^4+b^4)-ab(a^2+b^2)+(ab)^2
其中
a^2+b^2
=(a+b)^2-2ab
=1+2
=3
a^4+b^4
=(a^2+b^2)^2-2a^2b^2
=9-2
=7
因此，原式
=(a^4+b^4)-ab(a^2+b^2)+(ab)^2
=7+3+1
=11

Answer 3

a^2+b^2=(a+b)^2-2ab=1+2=3
a^3+b^3=(a+b)(a^2-ab+b^2)=4
(a^2+b^2)(a^3+b^3)=a^5+b^5+a^2b^2(a+b)=a^5+b^5+1=12

a^5+b^5=11