document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116943>Question 116943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Number problems. Find two consecutive positive integers such that the sum of their squares is 85. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85011 by </B><A HREF=/tutors/aboutme.mpl?userid=ganesh><B>ganesh(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ganesh><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x and x +1 be two consecutive positive numbers.\r<BR>\n" );
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document.write( "The square of the first number is x^2.\r<BR>\n" );
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document.write( "The square of the second number is, (x+1)^2 = x^2 + 2x + 1.\r<BR>\n" );
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document.write( "The sum of the squares of the two numbers = x^2 + x^2 + 2x + 1<BR>\n" );
document.write( "                                          = 2x^2 + 2x + 1\r<BR>\n" );
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document.write( "Given that, the sum of the squares is 85. \r<BR>\n" );
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document.write( "Therefore, 2x^2 + 2x + 1 = 85.\r<BR>\n" );
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document.write( "Or, 2x^2 + 2x - 84 = 0.\r<BR>\n" );
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document.write( "Solve this quadratic equation.   \r<BR>\n" );
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document.write( "2x^2 + 14x -12x - 84 = 0\r<BR>\n" );
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document.write( "2x (x +7) -12 (x +7) = 0\r<BR>\n" );
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document.write( "(x + 7)(2x - 12) = 0\r<BR>\n" );
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document.write( "x + 7 = 0   and 2x - 12 = 0\r<BR>\n" );
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document.write( "x = -7    and x = 6.\r<BR>\n" );
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document.write( "Since, x is given to be positive, it is 6.\r<BR>\n" );
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document.write( "So, the required consecutive numbers are 6 and 7.\r<BR>\n" );
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document.write( "Check: 6^2 + 7^2 = 36 + 49 = 85.\r<BR>\n" );
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document.write( "Good luck!<BR>\n" );
document.write( " </SPAN>\n" );
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