Question

已知x^2-3x+1=0，求x^3/(x^6+1)和x^5+(1/x^5)的值

如题，急求啊~~~

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 。