Problem:
If x+x2−1​+x−x2−1​1​=20 then x2+x4−1​+x2+x4−1​1​=
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−x2−1​1​=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+x4−1​1​​=x2+x4−1​+(x2−x4−1​)=2x2=21​⋅(10.1)2=51.005.​