数学题：如果x²-3X+1=0,求x^4+1/x^4的值

数学题：如果x²-3X+1=0,求x^4+1/x^4的值
数学题：如果x²-3X+1=0,求x^4+1/x^4的值

数学题：如果x²-3X+1=0,求x^4+1/x^4的值
等式两边同除以x
x-3+1/x=0
x+1/x=3
x^4+1/x^4
=(x²+1/x²)²-2
=[(x+1/x)²-2]²-2
=(9-2)²-2
=49-2
=47

x²-3x+1=0
x²+1=3x
x+1/x=3
(x+1/x)²=3²
x²+2+1/x²=9
x²+1/x²=7
(x²+1/x²)²=7²
x^4+2+1/x^4=49
x^4+1/x^4=47

先问一下，后面那个怪异的符号是什么意思

x^2-3X+1=0
x^2+1=3x
x^4+2x^2+1=9x^2
x^4+1=7x^2
x^4+1/x^4
=(x^2+1/x^2)^2-2(通分）
=((x^4+1)/x^2)^2-2
=（7x^2/x^2)^2-2
=49-2
=47