document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034425>Question 1034425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive positive numbers is 17/12. Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649066 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=649066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the first positive number equal x.<BR>\n" );
document.write( "then the second positive number equals x+1.\r<BR>\n" );
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document.write( "the sum of the reciprocals of those numbers is equal to 17/12.\r<BR>\n" );
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document.write( "you get 1/x + 1/(x+1) = 17/12.\r<BR>\n" );
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document.write( "multiply both sides of this equation by x * (x+1) to get:\r<BR>\n" );
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document.write( "(x+1) + x = 17/12 * (x+1) * x\r<BR>\n" );
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document.write( "simplify to get 2x + 1 = 17/12 * (x^2 + x)\r<BR>\n" );
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document.write( "multiply both sides of this equaiton by 12 to get:\r<BR>\n" );
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document.write( "12 * (2x + 1) = 17 * (x^2 + x)\r<BR>\n" );
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document.write( "simplify to get 24x + 12 = 17x^2 + 17x\r<BR>\n" );
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document.write( "subtract the left side of the equation from both sides of the equaiton to get:\r<BR>\n" );
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document.write( "0 = 17x^2 + 17x - 24x - 12.\r<BR>\n" );
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document.write( "simplify to get 0 = 17x^2 - 7x - 12.\r<BR>\n" );
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document.write( "this is the same as 17x^2 - 7x - 12 = 0.\r<BR>\n" );
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document.write( "solve this quadratic equation using the quadratic formula to get:\r<BR>\n" );
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document.write( "x = (7 + sqrt(865))/34 or x = (7 - sqrt(865))/34\r<BR>\n" );
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document.write( "this results in x = 1.070908304 or x = -.6591435982.\r<BR>\n" );
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document.write( "x  can't be negative, so x has to be equal to 1.070908304.\r<BR>\n" );
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document.write( "this makes x + 1 = 2.070908304.\r<BR>\n" );
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document.write( "if you did this correctly, you will get 1/1.070908304 + 1/2.070908304 = 17/12.\r<BR>\n" );
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document.write( "evaluate the left side of this equation to get 1.416666667 = 17/12.\r<BR>\n" );
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document.write( "multiply both sides of this equation by 12 to get 17 = 17.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "your positive consecutive numbers are 1.070908304 and 2.070908304.\r<BR>\n" );
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document.write( "these are the same as (7+sqrt(865))/34 and 1 + (7 + sqrt(865))/34.\r<BR>\n" );
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document.write( "1 + (7 + sqrt(865))/34 can also be written as (41+sqrt(865))/34.\r<BR>\n" );
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document.write( "you can solve the quadratic equation graphically as well.\r<BR>\n" );
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document.write( "i used the quadratic formula to get an exact answer.<BR>\n" );
document.write( "the graphing software i used gave me an approximate answer.<BR>\n" );
document.write( "that graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/051403.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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