[MOVED] If A = 2^x + 2^-x and B = 2^x - 2^-x then

[Guest]

If A = 2^x + 2^-x and B = 2^x - 2^-x then (A-B) (B-A) = ?

I work it out to be 4.

Working out:

(2^x + 2^-x -2^x +2^-x)(2^x - 2^-x-2^x + 2^-x)
(2.2^x)(2.2^-x)
=2 times 2^x times 2/2^x = 4.

 

[skeeter]

A - B = 2^-x + 2^-x = 2(2^-x) = 2^1-x

B - A = -2^-x - 2^-x = -2(2^-x) = -2^1-x

(A - B)(B - A) =
(2^1-x)(-2^1-x) =
-(2^1-x)(2^1-x) =
-2^(1-x)+(1-x) =
-2^2(1-x) =
-4^1-x