document.write( "Question 290858: The sum of a number and its reciprocal is 10/3 . what is the number? Also need to know how to check it.Thank you a bunch! \n" ); document.write( "
Algebra.Com's Answer #210447 by stanbon(75887)\"\" \"About 
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The sum of a number and its reciprocal is 10/3 . what is the number? Also need to know how to check it.Thank you a bunch!
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\n" ); document.write( "Equation:
\n" ); document.write( "x + 1/x = 10/3
\n" ); document.write( "---
\n" ); document.write( "Multiply thru by 3x to get:
\n" ); document.write( "3x^2 + 3 = 10x
\n" ); document.write( "---
\n" ); document.write( "Rearrange:
\n" ); document.write( "3x^2 - 10x + 3 = 0
\n" ); document.write( "Factor:
\n" ); document.write( "3x^2 - 9x - x + 3 = 0
\n" ); document.write( "3x(x-3)-(x-3) = 0
\n" ); document.write( "(x-3)(3x-1) = 0
\n" ); document.write( "Positive solution:
\n" ); document.write( "x = 1/3
\n" ); document.write( "---------
\n" ); document.write( "Checking:
\n" ); document.write( "x + (1/x) = 10/3
\n" ); document.write( "(1/3) + 3 = 10/3
\n" ); document.write( "(1/3)+(9/3) = 10/3
\n" ); document.write( "10/3 = 10/3
\n" ); document.write( "=============
\n" ); document.write( "Cheers,
\n" ); document.write( "stan H. \n" ); document.write( "
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