x²-2x-1=0,y²-2y-1=0
所以可以把x、y看成關于m的方程m²-2m-1=0的兩個根
根據(jù)根與系數(shù)的關系,得：x+y=2,xy=-1
所以(x+y)²=x²+y²+2xy=4,所以x²+y²=6
所以x^6+y^6=(x²+y²)(x^4-x²y²+y^4)
=(x²+y²)[(x²+y²)²-3x²y²]
=(x²+y²)[(x²+y²)²-3(xy)²]
=6×(36-3)
=198