document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=898355>Question 898355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference of two numbers is 7 and the sum of their squares is 137.<BR>\n" );
document.write( "Find the numbers.\r<BR>\n" );
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document.write( "The sum of two numbers is 8; the square of the first minus twice the<BR>\n" );
document.write( "square of the second equals 7. Find them.\r<BR>\n" );
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document.write( "Find two numbers that differ by 8 and whose product is 273.\r<BR>\n" );
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document.write( "There is a rectangle whose perimeter is 46 meters and whose area is<BR>\n" );
document.write( "112 square meters. What are its dimensions?\r<BR>\n" );
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document.write( "The sum of the areas of two squares is 325 square meters. The side of<BR>\n" );
document.write( "one increased by the side of the other is 25 meter. Find the length of a<BR>\n" );
document.write( "side of each.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #544784 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=544784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The difference of two numbers is 7 and the sum of their squares is 137.<BR>\n" );
document.write( "Find the numbers.\r<BR>\n" );
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document.write( "(x-y)=7<BR>\n" );
document.write( "(x-y)^2=49\r<BR>\n" );
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document.write( "x^2+y^2= 137\r<BR>\n" );
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document.write( "(x-y)^2+2xy = 137\r<BR>\n" );
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document.write( "7^2+2xy=137<BR>\n" );
document.write( "2xy= 137-49<BR>\n" );
document.write( "2xy=88<BR>\n" );
document.write( "xy=44\r<BR>\n" );
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document.write( "x-y=7\r<BR>\n" );
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document.write( "x=44/y\r<BR>\n" );
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document.write( "44/y -y = 7\r<BR>\n" );
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document.write( "44-y^2= 7y\r<BR>\n" );
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document.write( "y^2+7y-44=0\r<BR>\n" );
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document.write( "y^2+11y-4y-44=0\r<BR>\n" );
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document.write( "y(y+11)-4(y+11)=0<BR>\n" );
document.write( "(y+11)(y-4)=0\r<BR>\n" );
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document.write( "y=-11 OR 4 \r<BR>\n" );
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document.write( "x-y=7<BR>\n" );
document.write( "if y=-11<BR>\n" );
document.write( "x+11=7<BR>\n" );
document.write( "x=-4<BR>\n" );
document.write( "(-11, -4)\r<BR>\n" );
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document.write( "if y=4<BR>\n" );
document.write( "x=11\r<BR>\n" );
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document.write( "(11,4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The sum of two numbers is 8; the square of the first minus twice the<BR>\n" );
document.write( "square of the second equals 7. Find them.\r<BR>\n" );
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document.write( "one number be x <BR>\n" );
document.write( "other number = (8-x)\r<BR>\n" );
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document.write( "x^2-2(8-x)^2=7<BR>\n" );
document.write( "x^2-2(64-16x+x^2)=7<BR>\n" );
document.write( "x^2-128+32x-2x^2=7\r<BR>\n" );
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document.write( "-x^2+32x-135=0\r<BR>\n" );
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document.write( "x^2-32x+135=0\r<BR>\n" );
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document.write( "x^2-27x-5x+135=0<BR>\n" );
document.write( "x(x-27)-5(x-27)=0\r<BR>\n" );
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document.write( "(x-27)(x-5)=0<BR>\n" );
document.write( "x=5 OR 27<BR>\n" );
document.write( "xnot equal to 27<BR>\n" );
document.write( "x= 5 \r<BR>\n" );
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document.write( "(5,2)\r<BR>\n" );
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document.write( "Find two numbers that differ by 8 and whose product is 273.\r<BR>\n" );
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document.write( "x & 8+x<BR>\n" );
document.write( "x(8+x)=273<BR>\n" );
document.write( "8x+x^2=273<BR>\n" );
document.write( "x^2+8x -273=0<BR>\n" );
document.write( "x^2+21x-13x-273=0<BR>\n" );
document.write( "x(x+21)-13(x+21)=0\r<BR>\n" );
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document.write( "(x+21)(x-13)=0<BR>\n" );
document.write( "x=-21 OR 13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There is a rectangle whose perimeter is 46 meters and whose area is<BR>\n" );
document.write( "112 square meters. What are its dimensions?\r<BR>\n" );
document.write( "\n" );
document.write( "The sum of the areas of two squares is 325 square meters. The side of<BR>\n" );
document.write( "one increased by the side of the other is 25 meter. Find the length of a<BR>\n" );
document.write( "side of each.<BR>\n" );
document.write( " </SPAN>\n" );
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