document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134880>Question 1134880</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not sure how to do the problem which I will write down. I hope you can help me. Thank you in advance.\r<BR>\n" );
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document.write( "The sum of a number and its reciprocal is 17/4.  Find the number.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752383 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the number be x.\r<BR>\n" );
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document.write( "it's reciprocal would then be 1/x\r<BR>\n" );
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document.write( "you are given that the sum of the number and its reciprocal is equal to 17/4.\r<BR>\n" );
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document.write( "that means that x + 1/x = 17/4\r<BR>\n" );
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document.write( "place the expression on the left side of this equation under a common denominator and the equation becomes:\r<BR>\n" );
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document.write( "(x^2 + 1) / x = 17 / 4\r<BR>\n" );
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document.write( "cross multiply to get (x^2 + 1) * 4 = x * 17\r<BR>\n" );
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document.write( "simplify to get 4 * x^2 + 4 = 17 * x\r<BR>\n" );
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document.write( "subtract 17 * x from both sides of the equation to get 4 * x^2 - 17 * x + 4 = 0\r<BR>\n" );
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document.write( "factor this equation to get  (4x-1) * (x-4) = 0\r<BR>\n" );
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document.write( "solve for x to get x = 1/4 or x = 4.\r<BR>\n" );
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document.write( "if you let x = 4, then its reciprocal is 1/4 and 4 + 1/4 is equal to 17/4.\r<BR>\n" );
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document.write( "if you let x = 1/4, then its reciprocal is 4 and 1/4 + 4 = 17/4.\r<BR>\n" );
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document.write( "the number can either be 4 or 1/4.\r<BR>\n" );
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document.write( "either one will get you the correct answer.\r<BR>\n" );
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