12X的四次方-56X三次方+89X的二次方-56X+12=0

因为12X^4-56X^3+89X^2-56X+12=0,
所以12X^2-56X+89-(56/X)+(12/X^2)=0,
所以12X^2+(12/X^2)-[56X+(56/X)]+89=0,
所以12[X^2+(1/X^2)]-56[X+(1/X)]+89=0,
所以12{[X+(1/X)]^2-2}-56[X+(1/X)]+89=0,
所以12[X+(1/X)]^2-56[X+(1/X)]+65=0,
所以{2[X+(1/X)]-5}{6[X+(1/X)]-13}=0,
所以X+(1/X)=5/2或X+(1/X)=13/6,
所以X1=2,X2=1/2,X3=3/2,X4=2/3.

12x^4-56x^3+89x^2-56x+12
=12(x^4+1)-56x(x²+1)+89x²
=12(x²+1)²-56x(x²+1)+65x²
=[2(x²+1)-5x][6(x²+1)-13x]
=(x-2)(2x-1)(2x-3)(3x-2)