x+y=1 x^ +y^ =2,求x^5+y^5

Question

是 x^2 +y^ 2=2

Answer 1

(x+y)²=x²+y²+2xy=1，xy=-1/2，(x+y)³=x³+y³+3xy(x+y)=1，x³+y³=5/2，(x²+y²)²=4，
x^4 +y^4=7/2，(x+y)(x^4 +y^4)=x^5+y^5+xy(x³+y³)，x^5+y^5-1/2*5/2=7/2，x^5+y^5=19/4

Answer 2

x+y=1
x^2+y^2=2 (1)

(x+y)^2=1
x^2+2xy+y^2=1
xy=[1-(x^2+y^2)]/2=-1/2 (2)

(x+y)^3=1
x^3+y^3+3xy(x+y)=1
x^3+y^3=1-3xy(x+1)=1+3/2=5/2 (3)

(1)*(3)
x^5+y^5+(xy)^2(x+y)=5
x^5+y^5=5-(xy)^2(x+1)=5-1/4=19/4

Answer 3

此题无解，2元2次，不可能