Question

一道初二数学题

已知（x²-x+1)分之x=7，求（x的四次方+x²+1）分之x²的值

Answer 1

x/(x^2-x+1)=7
1/(x-1+1/x)=7
x-1+1/x=1/7
x+1/x=8/7

x^2/(x^4+x^2+1)
=1/(x^2+1+1/x^2)
=1/[(x+1/x)^2-1]
=1/[(8/7)^2-1]
=1/(15/49)
=49/15