Problem: If x=tt−11​ and y=tt−1t​,t>0,tî€ =1, a relation between x and y is:
Answer Choices:
A. yx=xy1​
B. yx1​=xy
C. yx=xy
D. xx=yy
E. none of these
Solution:
Method I.
​x=tt−11​,y=tt−11​=t1+t−11​=t⋅tt−11​∴y=tx. Also y=t(t−11​)t=xtyx=(xt)x=xtx∴yx=xy.​
Method II. x=tt−11​,y=tt−1t​∴xy​=tt−1t​⋅t−11​=t∴x=(xy​)y/x−11​=(xy​)x−yx​
∴xy−x=xxyx​∴xy=yx