解：∵ x²-3x+1=0∴ x²+1=3x(x²+1)×1/x=3x×1/x∴ x+(1/x)=3∴ [x+(1/x)]²=3²x²+2×x×1/x+(1/x²)=9x²+2+(1/x²)=9∴ x²+(1/x²)=7∴ [x²+(1/x²)]²=7²x^4+2×x²×(1/x²)+(1/x^4)=49 ( ^ 表示乘方)x^4+2+(1/x^4)=49∴ x^4+(1/x^4)=424
