Question

已知x/(xx+x+1)=a,求xx/(xxxx+xx+1)的值

Answer 1

x/(xx+x+1)=a分子分母除以x,

1/(x+1+1/x)=a,

x+1/x=1/a -1,两边平方

xx +2+ 1/xx=(1/a-1)^2

xx+ 1/xx=(1/a-1)^2-2

xx/(xxxx+xx+1)分子分母除以xx

=1/(xx+1/xx+1)

=1/〔(1/a-1)^2-2+1〕

=1/〔(1/a-1)^2-1〕

=a^2/(1-2a) .