已知x+y=-1,xy=-5求x五次方+y五次方的值好的绝对追加!

Question

已知x+y=-1, xy=-5 求x五次方+y五次方的值 好的绝对追加!

Answer 1

关键是因式分解
（x+y）²=1
x²+2xy+y²=1
x²+y²=1-2xy=11
(x+y)^3=(x+y)(x²-xy+y²)=-(11+5)=-16

(x²+y²)(x^3+y^3)=x^5+x^3y²+x²y^3+y^5=1x-16=-16
x^5+y^5=-16-x^3y²-x^3y^3=-16-x²y²(x+y)=-16+x²y²=-16+(xy)²=-16+25=9