那位数学高手帮忙解答`?(要过程)

a+b=1,
(a+b)^2=1
a^2+b^2+2ab=1

因为a^2+b^2=2，所以a^2+b^2+2ab=2+2ab=1
ab=-1/2

(a^2+b^2)^2=a^4+b^4+2(ab)^2=a^4+b^4+1/2=2^2
a^4+b^4=7/2
(a+b)(a^4+b^4)=1*7/2
a^5+b^5+ab^4+a^4b=7/2
a^5+b^5+ab(a^3+b^3)=7/2
a^5+b^5-1/2(a+b)(a^2+b^2-ab)=7/2
a^5+b^5-1/2(2+1/2)=7/2

a^5+b^5=7/2+5/4=19/4

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

ab=-0.5

(a+b)(a^2+b^2)^2=(a+b)(a^4+b^4+2a^2b^2)
=a^5+b^5+2(ab)^2(a+b)+ab(a^3+b^3)
=a^5+b^5+2(-0.5)^2-0.5[(a+b)(a^2+b^2)-ab(a+b)]
=a^5+b^5+0.5-0.5[2+0.5]=a^5+b^5-0.75=(a+b)(a^2+b^2)^2=4

a^5+b^5=4.75

因为a+b=1 所以(a+b)^2=a^2+2ab+b^2=1
因为a^2+b^2=2 所以2ab=1-2=-1 ab= -1/2
因为(a^2+b^2)^2=a^4+b^4+2(a^2b^2)=4 a^2b^2=(ab)^2=1/4
所以a^4+b^4=4-2*(a^2b^2)=4-2*1/4=7/2
因为(a^2+b^2)(a+b)=a^3+ab(a+b)+b^3=2*1=2
所以a^3+b^3=2-ab(a+b)=2-(-1/2)*1=5/2
因为(a^4+b^4)(a+b)=a^5+b^5+ab(a^3+b^3)=7/2
所以a^5+b^5=7/2-ab(a^3+b^3)=7/2-(-1/2)(5/2)=19/4