x^2-5x+1=0. 两边同时除以x. 得 x-5+1/x=0. x+1/x=5. x^2+1/x^2=(x+1/x)^2-2=23 x^2-5x+1=0,则x^2=5x-1 2x^2-5x+1/x^2 =10x-2-5x+1/(5x-1) =(5x-1)+1/(5x-1)-2 =x^2+1/x^2-2 =23-2=21
