两边平方
x^2+2xy+y^2=1
xy=（1-2）/2=-1/2
x^2+y^2=2
两边平方
x^4+2x^2y^2+y^4=4
x^4+y^4=4-2(xy)^2=7/2
x^3+y^3=(x+y)(x^2-xy+y^2)=5/2
x^5+y^5=(x+y)(x^4+y^4)-(x^4y+xy^4)
=(x+y)(x^4+y^4)-xy(x^3+y^3)
=1*7/2-(-1/2)(5/2)
=19/4=4.75本回答被提问者采纳
所以xy=-1/2
（x+y)(x^2+y^2)=x^3+y^3+xy(x+y)=2
所以x^3+y^3=-xy(x+y)+2=5/2
又x^4+y^4=(x^2+y^2)^2-2x^2*y^2=7/2
（x+y)(x^4+y^4)=x^5+y^5+xy(x^3+y^3)=7/2
所以x^5+y^5=-xy(x^3+y^3)+7/2=19/4
两边平方
x^2+y^2+2xy=1
xy=[1-(x^2+y^2)]/2=-1/2
x^3+y^3=(x+y)(x^2-xy+y^2)=1*(2-1)=1
所以x^5+y^5
=(x^3+y^3)(x^2+y^2)-x^3y^2-x^2y^3
=(x^3+y^3)(x^2+y^2)-(xy)^2(x+y)
=1*2-(-1/2)^2*1
=2-1/4
=7/4
得（y-1)^2=0
所以x=y=1
所以x^5+y^5=2
RT
若x+y=1,x^2+y^2=2,求x^5+y^5的值
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