SOLUTION: Please help me solve this equation: simplify {{{ (2+ (ae^4x-ae^-4x)/(e^x-e^-x)(ae^x+ae^-x))^1/2 = 2 }}}

Algebra ->  Exponents -> SOLUTION: Please help me solve this equation: simplify {{{ (2+ (ae^4x-ae^-4x)/(e^x-e^-x)(ae^x+ae^-x))^1/2 = 2 }}}      Log On


   

Question 744143: Please help me solve this equation: simplify +%282%2B+%28ae%5E4x-ae%5E-4x%29%2F%28e%5Ex-e%5E-x%29%28ae%5Ex%2Bae%5E-x%29%29%5E1%2F2+=+2+
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Take out common factor a.
Simplify, cancelling a's.
Recognize and use difference of squares special products %28b%2Bc%29%28b-c%29=b%5E2-c%5E2
Factors e%5E%282x%29-e%5E%28-2x%29 in numerators and denominator cancel out.
+%282%2B+e%5E%282x%29%2Be%5E%28-2x%29%29%5E%281%2F2%29+=+2+ Recognize square of binomial e%5Ex%2Be%5E%28-x%29
+%28%28e%5Ex%2Be%5E%28-x%29%29%5E2%29%5E%281%2F2%29+=+2+
+e%5Ex%2Be%5E%28-x%29+=+2+ --> x=0 (It's the minimum of the function)
If you know about hyperbolic functions, you may write the last equation as
2%2Acosh%28x%29=2 <--> cosh%28x%29=1