Question

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

Answer 1

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