How do you solve for x: in #2^x + 2^-x = 5/2#?

1 Answer
Jorge G. Pires · Alan P.
May 14, 2016

#x=+-1#

Explanation:

(I'm hoping that someone will come up with a better method of solving, since the following is simply "solution by observation").

We are told: #2^x+2^(-x)=5/2#

Observe that
#color(white)("XXXX")5/2 = 4/2 + 1/2#

#color(white)("XXXXX")=2 + 1/2#

#color(white)("XXXXX")=2^1+1/2^1#

#color(white)("XXXXX")=2^1+2^(-1)#

So #2^x+2^(-x)=2^1+2^(-1) =2^-1+2^1#
which implies

#color(white)("XXX")x=+-1#

Graph

Another possible way is looking at a graph

Graph for #2^x+2^(-x)#

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