Question

已知x^2-3x+1=0 求x^3/x^6+3x^3+1

Answer 1

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 .