2^(x) + 2^(-x) = 5/2

[joey.saad]

I know the answer is 1 just by looking at it, but for the life of me I cannot prove it algebraically. Help appreciated.

Thanks

[mathew.linoy]

2^(x) + 2^(-x) = 5/2

=> 2^(x) + 1/2^(x) = 5/2

(4x^2+1)/2x = 5/2
4x^2+1=5x
4x^2-5x+1=0
(4x-1)(x-1)

x=1/4 or x=1

[mgodwin16]

Can you break down how you got this part please?

(4x^2+1)/2x = 5/2

Thanks

[joey.saad]

2^(x) + 2^(-x) = 5/2

=> 2^(x) + 1/2^(x) = 5/2

(4x^2+1)/2x = 5/2
4x^2+1=5x
4x^2-5x+1=0
(4x-1)(x-1)

x=1/4 or x=1

How did you rearrange to the bold step?

[tim]

mathew's explanation was pretty much all wrong. here's how to do it:

2^x + 2^-x = 5/2

let u = 2^x

u + 1/u = 5/2
2u^2 + 2 = 5u
2u^2 - 5u + 2 = 0
(2u - 1)(u - 2) = 0
u = 1/2 or 2
2^x = 1/2 or 2
x = 1 or -1

[mathew.linoy]

Ohh yess. I am sorry. :-)

[tim]

no worries. just remember to be careful with your own calculations..