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
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![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](/uploads/image/z/997091-35-1.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%A4%E4%B8%AA%E4%B8%8D%E5%90%8C%E5%AE%9E%E6%95%B0x%E3%80%81y%E6%BB%A1%E8%B6%B3x%26%23178%3B%3Dx%2B1%2Cy%26%23178%3B%3Dy%2B1%2C%E5%88%99x%E7%9A%84%E8%B4%9F%E4%BA%94%E6%AC%A1%E6%96%B9%E5%8A%A0%E4%B8%8Ay%E8%B4%9F%E4%BA%94%E6%AC%A1%E6%96%B9%E7%9A%84%E5%80%BC%E6%98%AF)
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