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)=47
