Question

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

Answer 1

`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