Question

已知x/(x^2+x+1)=a求x^2/(x^4+x^2+1)的值

Answer 1

x/(x^2+x+1)=a 同时平方

x^2/(x^4+2x^3+3x^2+2x+1)=a^2

x^2/[(x^4+x^2+1)+2x(x^2+x+1)]=a^2 同时被1除

[(x^4+x^2+1)+2x(x^2+x+1)]/x^2=1/a^2

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

x^4+x^2+1/x^2+2/a=1/a^2

x^4+x^2+1/x^2=1/a^2-2/a=1-2a/a^2 同时被1除

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