由 x²-3x+1=0 ，可得：x+1/x = 3 ，x²+1/x² = (x+1/x)²-2 = 7 ，x³+1/x³ = (x+1/x)(x²+1/x²)-(x+1/x) = 18 ，所以，x^3/(x^6+1) = 1/(x³+1/x³) = 1/18 ；x^5+1/x^5 = (x²+1/x²)(x³+1/x³)-(x+1/x) = 123 。
