已知x+y=4,xy=1,求x^5+y^5
发布网友
发布时间：2024-10-24 02:42
共2个回答
热心网友
时间：2024-11-03 21:24
解：x^2+y^2=(x+y)^2-2xy=14
x^3+y^3=(x+y)(x^2-xy+y^2)=(x+y)((x+y)^2-3xy)=4*(16-3)52
x^5+y^5=(x+y)(x^4-x^3y+x^2y^2-xy^3+y^4)
=(x+y)((x^2+y^2)^2-x^2y^2-xy(x^2+y^2))
=4*(14^2-1-14)
=4*181
=724
热心网友
时间：2024-11-03 21:25
x+y=4,
x^2+y^2=4^2-2=14
x^4+y^4=14^2-2=194
(x^2+y^2)(x^4+y^4)=x^6+x^2y^2(x^2+y^2)+y^6=x^6+y^6+14
14*194=x^6+y^6+14
x^6+y^6=193*14=2702
x^5+y^5=(x+y)(x^5+y^5)=x^6+y^6+xy(x^4+y^4)=2702+194=26
希望你能看懂，你能明白
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