document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117950>Question 117950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two integers, x and x + 1, whose squares differ by 25. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85979 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=85979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The two unknown integers are represented by x and by x+1<BR>\n" );
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document.write( "If you square the two integers you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Squaring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2+=+%28x%2B1%29%2A%28x%2B1%29+=+x%5E2+%2B+2x+%2B+1 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2+=+%28x%2B1%29%2A%28x%2B1%29+=+x%5E2+%2B+2x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you subtract the two squares, the problem tells you that the result is 25. In equation form<BR>\n" );
document.write( "this subtraction can be expressed as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+%2B1+-+x%5E2+=+25 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+%2B1+-+x%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that in the subtraction the two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms are of opposite sign and therefore<BR>\n" );
document.write( "cancel each other. Therefore, you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+1+=+25 ALIGN=MIDDLE  ALT=\"2x+%2B+1+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 1 on the left side by subtracting 1 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+24 ALIGN=MIDDLE  ALT=\"2x+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for x by dividing both sides of this equation by 2 to reduce the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24%2F2+=+12 ALIGN=MIDDLE  ALT=\"x+=+24%2F2+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So one of the unknown integers (that is x) equals 12. The other integer is x + 1 and therefore<BR>\n" );
document.write( "it equals 12 + 1 or 13.<BR>\n" );
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document.write( "The two integers you are looking for are 12 and 13.<BR>\n" );
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document.write( "Check. 12 squared is 144 and 13 squared is 169. The difference is 169 - 144 = 25, just as the<BR>\n" );
document.write( "problem requires. So this answer checks and the two integers are 12 and 13.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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