document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48164>Question 48164</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534373526/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find all solutions of the system of equations\r<BR>\n" );
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document.write( "xy=24<BR>\n" );
document.write( "2x^2-y^2+4 = 0\r<BR>\n" );
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document.write( "Thank you so very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31882 by </B><A HREF=/tutors/aboutme.mpl?userid=deepblue><B>deepblue(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=deepblue><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=31882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> HI freind,\r<BR>\n" );
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document.write( "these equations generally lead to quadratic equations\r<BR>\n" );
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document.write( "given xy=24 and 2x^2-y^2+4=0\r<BR>\n" );
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document.write( "in the second eqn substitute y=24/x<BR>\n" );
document.write( "u get,\r<BR>\n" );
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document.write( "2x^2-(24/x)^2+4=0\r<BR>\n" );
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document.write( "simplifying we get 2x^4+4x^2-(24)^2=0\r<BR>\n" );
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document.write( "now assume x^2=p and substitute in teh above eqn we get\r<BR>\n" );
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document.write( "2p^2+4p-(24)^2=0\r<BR>\n" );
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document.write( "which is a normal quadratic equation\r<BR>\n" );
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document.write( "whose solutions are<BR>\n" );
document.write( "p=16 and p=-18\r<BR>\n" );
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document.write( "case 1:x^2=p=16\r<BR>\n" );
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document.write( "=>  x=+sqrt(p) or - sqrt(p) =+4 or -4\r<BR>\n" );
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document.write( "case 2:when x^2=p=-18\r<BR>\n" );
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document.write( "x=- sqrt(-18)or + sqrt(-18)<BR>\n" );
document.write( "   =-4.24i  or   4.24i  (we know sqrrt(-1)=i)\r<BR>\n" );
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document.write( "hence we have four slutions\r<BR>\n" );
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document.write( "two are real and otehr two are complex!\r<BR>\n" );
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document.write( "now having got x , y=24/x\r<BR>\n" );
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document.write( "so values of y follow (but take care! x=0 can never be a solution! if x=0 then y=24/x becomes 24/0....which is undefined!)\r<BR>\n" );
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document.write( "hope i solved ur question!\r<BR>\n" );
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document.write( "take care </SPAN>\n" );
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