Question

如果x=x分之1,求分式x平方+3分之x四次方+x平方-6 因式分解：x4-x2-x+1

Answer 1

∵x=1/x ∴x平方=1
(x4+x2-6)/(x2+3)=[(x2)2+1-6]/4=(1+1-6)/4=-1
x4-x2-x+1=x(x3-1)-(x2-1)
=x(x-1)(x2+x+1)-(x-1)(x+1)
=(x-1)(x3+x2+x-x-1)
=(x-1)(x3+x2-1)