document.write( "Question 320138: The sum of a number and it's reciprocal is 10/3. What is the number ? \n" ); document.write( "
Algebra.Com's Answer #229279 by CharlesG2(834)\"\" \"About 
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The sum of a number and it's reciprocal is 10/3. What is the number ?\r
\n" ); document.write( "\n" ); document.write( "let x = the number
\n" ); document.write( "let 1/x = the reciprocal of the number\r
\n" ); document.write( "\n" ); document.write( "x + 1/x = 10/3
\n" ); document.write( "x^2 + 1 = (10/3)x (multiplied both sides by x)
\n" ); document.write( "x^2 - (10/3)x = -1
\n" ); document.write( "x^2 - (10/3)x + (-5/3)^2 = -1 + (-5/3)^2 (completed the square)
\n" ); document.write( "(x - 5/3)(x - 5/3) = x^2 - (5/3)x - (5/3)x + (-5/3)^2 (by use of FOIL)
\n" ); document.write( "(x - 5/3)^2 = -1 + 25/9 = -9/9 + 25/9 = 16/9
\n" ); document.write( "x - 5/3 = 4/3
\n" ); document.write( "x = 9/3 = 3
\n" ); document.write( "its reciprocal 1/x = 1/3\r
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