已知正数x满足x的4次方减7x的平方加1等于0,求x的三次方加x的三次方分之1的值

x的4次方减7x的平方加1等于0
x^4-7x^2+1=0
x^2-7+1/x^2=0
x^2+1/x^2=7 x^2-1+1/x^2=6
x^2+2+1/x^2=9
(x+1/x)^2=9
x+1/x=±3
x的三次方加x的三次方分之1
=x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
=(±3)*6
=±18