x²+x+1分之x=a则x的四次方+x²+1分之x²的值_其他解答

x²+x+1分之x=a则x的四次方+x²+1分之x²的值

人气：457 ℃　时间：2019-08-22 20:33:03

解答

x/(x^2+x+1)=a
(x^2+x+1)/x=x+1/x+1=1/a
x+1/x=1/a-1
(x+1/x)^2=x^2+1/x^2+2=(1/a-1)^2
x^2+1/x^2=1/a^2-2/a-1
x^2/(x^4+x^2+1)
=1/(x^2+1+1/x^2)
=1/(1/a^2-2/a-1+1)
=1/(1/a^2-2/a)
=a^2/(1-2a)