document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167984>Question 1167984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. The square of a positive integer is 98 less than twice the square of the next consecutive integer. Find the integers. Show your solution.\r<BR>\n" );
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document.write( "2. Find two integers differ by 4, while their squares differ by 56. Show your solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792590 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <i>1. The square of a positive integer is 98 less than twice the square of the next consecutive integer. Find the integers.</i><BR>\n" );
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document.write( "First integer = x<BR>\n" );
document.write( "Second integer = x + 1<BR>\n" );
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document.write( "x² = 2(x + 1)² - 98<BR>\n" );
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document.write( "x² = 2(x² + 2x + 1) - 98<BR>\n" );
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document.write( "x² = 2x² + 4x + 2 - 98<BR>\n" );
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document.write( "x² = 2x² + 4x - 96<BR>\n" );
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document.write( "x² + 4x - 96 = 0<BR>\n" );
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document.write( "(x - 8)(x + 12) = 0<BR>\n" );
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document.write( "x = 8 and x = -12<BR>\n" );
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document.write( "Since the problem stated the integers were positive, we can eliminate the x = -12 result.  We are left with x = 8.  So...<BR>\n" );
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document.write( "First integer = x = <b>8</b><BR>\n" );
document.write( "Second integer = x + 1 = <b>9</b><BR>\n" );
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document.write( "==================================================================<BR>\n" );
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document.write( "<i>2. Find two integers differ by 4, while their squares differ by 56.</i><BR>\n" );
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document.write( "First integer = x<BR>\n" );
document.write( "Second integer = x + 4<BR>\n" );
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document.write( "(x + 4)² - x² = 56<BR>\n" );
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document.write( "x² + 8x + 16 - x² = 56<BR>\n" );
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document.write( "8x + 16 = 56<BR>\n" );
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document.write( "8x = 40<BR>\n" );
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document.write( "x = 5<BR>\n" );
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document.write( "First integer = x = <b>5</b><BR>\n" );
document.write( "Second integer = x + 4 = <b>9</b> </SPAN>\n" );
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