document.write( "Question 831629: e^x-e^-x=1 Hint:Multiply both sides by e^x.
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Algebra.Com's Answer #501622 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"e%5Ex-e%5E%28-x%29=1\"$
\n" ); document.write( " $\"e%5E%282x%29-1=e%5Ex\"$
\n" ); document.write( " $\"e%5E%282x%29-e%5Ex-1=0\"$
\n" ); document.write( "Let $\"u=e%5Ex\"$ , $\"u%5E2=e%5E%282x%29\"$ ,
\n" ); document.write( " $\"u%5E2-u-1=0\"$
\n" ); document.write( " $\"u+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"u+=+%281+%2B-+sqrt%28+1%2B4+%29%29%2F%282%29+\"$
\n" ); document.write( " $\"u+=+%281+%2B-+sqrt%285+%29%29%2F%282%29+\"$
\n" ); document.write( "Only the positive solution works in this case since $\"e%5Ex%3E0\"$
\n" ); document.write( " $\"e%5Ex=%281%2Bsqrt%285%29%29%2F2\"$
\n" ); document.write( " $\"highlight_green%28x=ln%281%2Bsqrt%285%29%29%2F2%29\"$
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2C+e%5Ex-e%5E%28-x%29%29+\"$ \n" ); document.write( "

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