Question

如果x平方-3x+1=0,求x4次方+x4次方分之一的值.

Answer 1

x平方-3x+1=0

二边同除以x

x-3+1/x=0

x+1/x=3

x^2+1/x^2=(x+1/x)^2-2=3^2-2=7

x^4+1/x^4=(x^2+1/x^2)^2-2=7^2-2=47