document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=20931>Question 20931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the squares of two positive consecutive odd integers is 394. Find the integer.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12124 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let any number be x ...then 2x will be always even....if we subtract 1 from it it will be always odd<BR>\n" );
document.write( "so 2x-1 is one odd number ..its next odd number will be 2x-1+2=2x+1<BR>\n" );
document.write( "so sum of their squares <BR>\n" );
document.write( "(2x-1)^2+(2x+1)^2=394<BR>\n" );
document.write( "2[(2x)^2+(1)^2]=394...using formula (a+b)^2+(a-b)^2=2[(a)^2+(b)^2]<BR>\n" );
document.write( "(4x^2+1)=394/2=197<BR>\n" );
document.write( "4x^2=197-1=196<BR>\n" );
document.write( "x^2=196/4=49<BR>\n" );
document.write( "x=7...hence the 2 numbers are 2*7-1=14-1=13 and 15...you can easily verify <BR>\n" );
document.write( "13^2=169<BR>\n" );
document.write( "15^2=225<BR>\n" );
document.write( "sum is 394<BR>\n" );
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