已知x^2-5x+1=0,求值x^5+1/x^5

Question

已知x^2-5x+1=0,求值x^5+1/x^5

Answer 1

因为x^2-5x+1=0所以x+1/x-5=0x+1/x=5 (1）x^2+1/x^2=23 （2）（1）*（2）（x+1/x)(x^2+1/x^2)=115x^3+1/x^3++x+1/x=115x^3+1/x^3=110 (3)(x^4+1/x^4)(x+1/x)=[(x^2+1/x^2)^2-2](x+1/x)x^5+1/x^5+x^3+1/x^3=[23^2-2)*...