Question

已知a+b=1，a^2+b^2=2，求a^7+b^7的值

Answer 1

a b=1
(a b)^2=1
a^2 b^2 2ab=1
2 2ab=1
ab=-0.5
a^2 b^2=2
(a^2 b^2)^2=4
a^4 b^4 2(ab)^2=4
a^4 b^4=3.5
(a^4 b^4)^2=12.25
a^8 b^8 2(ab)^4=12.25
a^8 b^8=12.125
a^6 b^6
=(a^2 b^2)[a^4 b^4-(ab)^2]
=2*(3.5-0.25)
=6.5
a^7 b^7
=(a^7 b^7)*(a b)
=a^8 b^8 ab^7 ba^7
=(a^8 b^8) ab(a^6 b^6)
=12.125 (-0.5)*6.5
=8.875