已知两个不同实数x、y满足x²=x+1,y²=y+1,则x的负五次方加上y负五次方的值是

已知两个不同实数x、y满足x²=x+1,y²=y+1,则x的负五次方加上y负五次方的值是
已知两个不同实数x、y满足x²=x+1,y²=y+1,则x的负五次方加上y负五次方的值是

已知两个不同实数x、y满足x²=x+1,y²=y+1,则x的负五次方加上y负五次方的值是
x²=x+1,
x=(1±√5)/2
y²=y+1,
y=(1±√5)/2
x≠y
x+y=(1+√5)/2+(1-√5)/2=1
x^5+y^5
=x²*x²*x+y²*y²*y
=(x+1)(x+1)*x+(y+1)(y+1)*y
=x(x²+2x+1)+y(y²+2y+1)
=x(x+1+2x+1)+y(y+1+2y+1)
=x(3x+2)+y(3y+2)
=3x²+2x+3y²+2y
=3(x+1)+2x+3(y+1)+2y
=5x+3+5y+3
=5(x+y)+6
=5*1+6
=11
x^5*y^5=[(1+√5)/2*(1-√5)/2]^5=-1
x^-5+y^-5=11/(-1)=-11