What is the solution to 2^x + 2^-x = 3?

[Andolph23]

The Attempt at a Solution

2^x + 2^-x = 3

2^x + (1 / ((2^x)) = 3

(4^((x^2)) +1) / (2^x) = 3

(4^((x^2)) + 1) = 6^ x

 

[HallsofIvy]

No, 2(3^x) is not the same 6^x.

 

[gb7nash]

Multiply both sides by 2^x instead.

 

[Andolph23]

My bad. I forgot that they must have the same base to multiply them. Also, If you're referring to the last step, I did multiply both sides by 2^x. I'm stuck at that point though.

 

[GreenPrint]

let u = 2^x
solve the quadratic
after solve for u solve for x

 

[Andolph23]

Thanks that helped a lot. Thanks everyone for the quick replies