几道数题目,着急!1.x^2-x-1=0,求x^5-5x的值.2.已知x+y=4,x^2+y^2=10,求x^3+y^3,x^4+y^4的值.3.已知x+5y=6,求x^2+5xy+30y的值

Question

几道数题目,着急!
1.x^2-x-1=0,求x^5-5x的值.
2.已知x+y=4,x^2+y^2=10,求x^3+y^3,x^4+y^4的值.
3.已知x+5y=6,求x^2+5xy+30y的值

Answer 1

(1)x^2-x-1=0(x^2-x+1/4)-1/4-1=0(x-1/2)^2-5/4=0x=(1±√5)/2x^5-5x=x(x^4-5)=〔(1±√5)/2〕｛〔(1±√5)/2〕^4 - 5｝=3(2)x^2+y^2=x^2+2xy+y^2-2xy=(x+y)^2-2xy=4^2-2xy=16-2xy=10xy=3x^3+y^3=(x+y)(x^2+xy+y^2)=...