document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1050872>Question 1050872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What 2 numbers add to get \"1\" and multiply to get \"5\"? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #666489 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=666489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) x + y = 1<BR>\n" );
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document.write( "2) x * y = 5<BR>\n" );
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document.write( "solve equation 1) for x<BR>\n" );
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document.write( "x = 1 - y<BR>\n" );
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document.write( "substitute for x in equation 2)<BR>\n" );
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document.write( "(1 - y) * y = 5<BR>\n" );
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document.write( "y - y^2 = 5<BR>\n" );
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document.write( "y^2 -y +5 = 0<BR>\n" );
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document.write( "solve for y by completing the square<BR>\n" );
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document.write( "y^2 -y = -5<BR>\n" );
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document.write( "y^2 -y +(1/4) = -5 +(1/4)<BR>\n" );
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document.write( "(y - (1/2))^2 = -19/4<BR>\n" );
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document.write( "y -(1/2) = square root(-19/4) = (i * square root(19))/2<BR>\n" );
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document.write( "y = (1 + i * square root(19)) / 2<BR>\n" );
document.write( "y = (1 - i * square root(19)) / 2<BR>\n" );
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document.write( "x = 1 - ((1 + i * square root(19)) / 2) = (1 - i * square root(19)) / 2<BR>\n" );
document.write( "x = 1 - ((1 - i * square root(19)) / 2) = (1 + i * square root(19)) / 2<BR>\n" );
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document.write( "we have two sets of solutions<BR>\n" );
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document.write( "x = (1 - i * square root(19)) / 2<BR>\n" );
document.write( "y = (1 + i * square root(19)) / 2<BR>\n" );
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document.write( "x = (1 + i * square root(19)) / 2<BR>\n" );
document.write( "y = (1 - i * square root(19)) / 2<BR>\n" );
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document.write( "checking answers<BR>\n" );
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document.write( "clearly x + y = 1<BR>\n" );
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document.write( "what about xy = 5<BR>\n" );
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document.write( "xy = (1 -(i^2 * 19)) / 4 = (1 - (-19)) / 4 = 20 / 4 = 5<BR>\n" );
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document.write( "our answers check   :-)<BR>\n" );
document.write( ":\r<BR>\n" );
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document.write( " </SPAN>\n" );
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