Problem:
If x+x2−1+x−x2−11=20 then x2+x4−1+x2+x4−11=
Answer Choices:
A. 5.05
B. 20
C. 51.005
D. 61.25
E. 400
Solution:
Clear the denominator in the first equation to obtain
(x2−(x2−1))+1=20(x−x2−1) or x−x2−1=101.
Thus x−x2−11=x+x2−1=10, so that 2x=101+10=10.1. Rationalize the denominator in the problem's second expression to obtain
x2+x4−1+x2+x4−11=x2+x4−1+(x2−x4−1)=2x2=21⋅(10.1)2=51.005.