document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=773965>Question 773965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem\r<BR>\n" );
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document.write( "prove that <BR>\n" );
document.write( "for all values ok k ,roots of this equation ( x^2-2((k)+(1/k))x+3=0) are real </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471981 by </B><A HREF=/tutors/aboutme.mpl?userid=oscargut><B>oscargut(2103)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oscargut><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=oscargut><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=471981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2-2((k)+(1/k))x+3=0\r<BR>\n" );
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document.write( "discriminant = d = (-2((k)+(1/k)))^2-4(1)(3) =\r<BR>\n" );
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document.write( "4(k^2+2+1/k^^2) -12\r<BR>\n" );
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document.write( "=  4k^2+8+4/k^2 -12\r<BR>\n" );
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document.write( "=  4k^2+4/k^2 -4\r<BR>\n" );
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document.write( "= 4(k^2+1/k^2 -1)\r<BR>\n" );
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document.write( "= 4 ((k-1/k)^2 +1) >0  \r<BR>\n" );
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document.write( "Then the equation has 2 real solutions\r<BR>\n" );
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document.write( "I can help you with more questions at: mthman@gmail.com\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
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