document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=551045>Question 551045</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two no. Are like that if they are added the product is 56 and when they 2 no. Are added with their squares the sum is 128 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #359334 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=359334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two no. Are like that if they are added the product is 56 and when they 2 no. Are added with their squares the sum is 128<BR>\n" );
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document.write( "I think you mean \"When two numbers are multiplied the product is 56\" and<BR>\n" );
document.write( "When the squares are added the sum is 128<BR>\n" );
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document.write( "Let the two number be a & b<BR>\n" );
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document.write( "when multiplied: a*b = 56<BR>\n" );
document.write( "When squares added: a^2 * b^2 = 128<BR>\n" );
document.write( "we can rearrange this to<BR>\n" );
document.write( "b^2 = 128 - a^2<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28128-a%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28128-a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then from the 1st equation<BR>\n" );
document.write( "a*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28128-a%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28128-a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 56<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "a^2(128-a^2) = 3136<BR>\n" );
document.write( "128a^2 - a^4 = 3176<BR>\n" );
document.write( "0 = a^4 - 128a^2 + 3136<BR>\n" );
document.write( "Using the quadratic formula we get two solutions<BR>\n" );
document.write( "a^2 = 33<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2833%29 ALIGN=MIDDLE  ALT=\"sqrt%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 5.746<BR>\n" );
document.write( "and<BR>\n" );
document.write( "a^2 = 95<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2895%29 ALIGN=MIDDLE  ALT=\"sqrt%2895%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 9.746<BR>\n" );
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document.write( "a = 5.746, then b = 9.746<BR>\n" );
document.write( "a = 9.746, then b = 5.746<BR>\n" );
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document.write( ":<BR>\n" );
document.write( "Check this in the original problem<BR>\n" );
document.write( "5.746 * 9.746 = 56.00<BR>\n" );
document.write( "and<BR>\n" );
document.write( "5.746^2 + 9.746^2 = 128.00 </SPAN>\n" );
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