Solve #a^(2x)-a^x-a^(x+1)+a=0# ?

1 Answer
Jan 22, 2018

See below.

Explanation:

We have

#(a^x)^2-(a+1)a^x+a=0# and solving for #a^x#

#a^x = 1/2((a+1)pmsqrt((a+1)^2-4a)) = 1/2((a+1)pmsqrt((a-1)^2)) = 1/2((a+1)pm(a-1)) = {(a),(1):}#

and now from

#a^x = {(a),(1):}#

we conclude

#x = {(1),(0):}#