document.write( "Question 1020933: 3^2x + 3^-2x = 14
\n" ); document.write( "3^x + 3^-x = ? \n" ); document.write( "

Algebra.Com's Answer #636734 by robertb(5830) $\"\"$ $\"About$

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The answer is 4.\r
\n" ); document.write( "\n" ); document.write( "To see why,
\n" ); document.write( " $\"3%5E%282x%29%2B3%5E%28-2x%29+=+14\"$ <==> $\"3%5E%282x%29%2B1%2F3%5E%282x%29+=+14\"$
\n" ); document.write( "<==> $\"3%5E%284x%29+%2B+1+=+14%2A3%5E%282x%29\"$
\n" ); document.write( "<==> $\"3%5E%284x%29+-+14%2A3%5E%282x%29%2B1+=+0\"$
\n" ); document.write( "By the quadratic formula, we then get \r
\n" ); document.write( "\n" ); document.write( " $\"3%5E%282x%29+=+%2814%2B-sqrt%28192%29%29%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( "<==> $\"3%5E%282x%29+=+7%2B-sqrt%2848%29\"$ ==> $\"3%5Ex+=+sqrt%287%2B-sqrt%2848%29%29\"$
\n" ); document.write( "(Note that these two values are inverses of each other, so that $\"3%5Ex%2B3%5E%28-x%29\"$ will have only one value, regardless whether we choose $\"3%5Ex+=+sqrt%287%2Bsqrt%2848%29%29\"$ or $\"3%5Ex+=+sqrt%287-sqrt%2848%29%29\"$ .)\r
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