document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119280>Question 119280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One number is 5 greater than another number. If The sum of their squares is 5 times the square of the smaller number, what are the numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87400 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=87400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One number is 5 greater than another number. If The sum of their squares is 5 times the square of the smaller number, what are the numbers?<BR>\n" );
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document.write( "Let x = \"One number\"<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x-5) = \"another number\"; (assume it is the smaller number)<BR>\n" );
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document.write( "\"If The sum of their squares is 5 times the square of the smaller number,\"<BR>\n" );
document.write( "x^2 + (x-5)^2 = 5(x-5)^2<BR>\n" );
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document.write( "Subtract (x-5)^2 from both sides:<BR>\n" );
document.write( "x^2 = 5(x-5)^2 - (x-5)^2<BR>\n" );
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document.write( "x^2 = 4(x-5)^2<BR>\n" );
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document.write( "x^2 = 4(x^2-10x+25)<BR>\n" );
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document.write( "x^2 = 4x^2 - 40x + 100<BR>\n" );
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document.write( "3x^2 - 40x + 100 = 0; subtracted x^2 from both sides<BR>\n" );
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document.write( "Factor this to:<BR>\n" );
document.write( "(3x - 10)(x - 10) = 0<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F3 ALIGN=MIDDLE  ALT=\"10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = 10; the integer solution is what we want here.<BR>\n" );
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document.write( "\"what are the numbers?\"<BR>\n" );
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document.write( "numbers are 10 and 5<BR>\n" );
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document.write( "Check solution using the statement:<BR>\n" );
document.write( "\"If The sum of their squares is 5 times the square of the smaller number,<BR>\n" );
document.write( "10^2 + 5^2 = 5(5^2)<BR>\n" );
document.write( "100 + 25 = 5(25); confirms our solution<BR>\n" );
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document.write( "Note the other solution x = 10/3 may also be a valid answer since they did not specify that they had to be integers.  Check that out.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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