document.write( "Question 48155: the sum of a number and its reciprocal is 10/3 what is the number? \n" ); document.write( "

Algebra.Com's Answer #31869 by Earlsdon(6294) $\"\"$ $\"About$

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Let n be the required number.\r
\n" ); document.write( "\n" ); document.write( " $\"n%2B%281%2Fn%29+=+10%2F3\"$ Simplift this.
\n" ); document.write( " $\"%28n%5E2%2B1%29%2Fn+=+10%2F3\"$ Multiply both sides by n.
\n" ); document.write( " $\"n%5E2%2B1+=+10n%2F3\"$ Multiply both sides by 3.
\n" ); document.write( " $\"3n%5E2%2B3+=+10n\"$ Subtract 10n from both sides.
\n" ); document.write( " $\"3n%5E2-10n%2B3+=+0\"$ Solve this quadratic equation by factoring.
\n" ); document.write( " $\"3n%5E2-10n%2B3+=+%283n-1%29%28n-3%29\"$ Apply the zero products principle.
\n" ); document.write( " $\"3n-1+=+0\"$ and/or $\"n-3+=+0\"$
\n" ); document.write( "If $\"3n-1+=+0\"$ then $\"3n+=+1\"$ and $\"n+=+1%2F3\"$
\n" ); document.write( "If $\"n-3+=+0\"$ then $\"n+=+3\"$ \r
\n" ); document.write( "\n" ); document.write( "The answer is there are two numbers that meet the given criteria:\r
\n" ); document.write( "\n" ); document.write( " $\"1%2F3\"$ and $\"3\"$ \n" ); document.write( "

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