Problem: If y=x+1/x, then x4+x3−4x2+x+1=0 becomes
Answer Choices:
A. x2(y2+y−2)=0
B. x2(y2+y−3)=0
C. x2(y2+y−4)=0
D. x2(y2+y−6)=0
E. none of these
Solution:
x4+x3−4x2+x+1=x2[(x2+x21)+(x+x1)−4]=0.
Since x2+x21=(x+x1)2−2, we have x2(y2−2+y−4)=x2(y2+y−6)=0.