已知x2-x+1\x=5\1求x⁴+x2+1\x2的值

已知x2-x+1\x=5\1求x⁴+x2+1\x2的值
已知x2-x+1\x=5\1求x⁴+x2+1\x2的值

已知x2-x+1\x=5\1求x⁴+x2+1\x2的值
x2-x+1\x=5\1
则
x-1+(1/x)=5
x+(1/x)=6
平方得
(x+1/x)²=36
x²+2+1/x²=36
x²+1/x²=34
x⁴+x2+1\x2
=1/(x²+1/x²+1)
=1/35

5\1还是1/5?