document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092206>Question 1092206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q. If x-1/x=3 find the value of <BR>\n" );
document.write( "1.  x^4+1/x^4  2. X^2+1/x^2  3. (X+1/x)^2\r<BR>\n" );
document.write( "\n" );
document.write( "Q. if a+1/a=7 find the value of <BR>\n" );
document.write( "1.a^2+1/a^2  2.(a-1/a)^2  3. a^4+1/a^4\r<BR>\n" );
document.write( "\n" );
document.write( "Q. If x+1/x=4, show that x^2+1/x^2=14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706793 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=706793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>I'll show you a couple of these so you can get the idea of how to work them.  Then you can try the others yourself.<br><BR>\n" );
document.write( "The last question is the easiest one to use to show you the general concept for working this kind of problem.  In that problem we are given<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1%2Fx+=+4 ALIGN=MIDDLE  ALT=\"x+%2B+1%2Fx+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and we are to show that<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+1%2Fx%5E2+=+14 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+1%2Fx%5E2+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Observe what happens when you square both sides of the given equation.  When you square the binomial on the left, the middle term is a constant.  That is the general principle that lets you solve problems like this.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+1%2Fx%29%5E2+=+4%5E2 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%2Fx%29%5E2+=+4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2+%2B+1%2Fx%5E2+=+16 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2+%2B+1%2Fx%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+1%2Fx%5E2+=+14 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+1%2Fx%5E2+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now let's look a bit at your second problem.  There you are given<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B1%2Fa+=+7 ALIGN=MIDDLE  ALT=\"a%2B1%2Fa+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and you are asked to find the values of<br><BR>\n" );
document.write( "1. a^2+1/a^2<BR>\n" );
document.write( "2.(a-1/a)^2<BR>\n" );
document.write( "3. a^4+1/a^4<br><BR>\n" );
document.write( "Finding the first of these will be exactly like the example worked above.  For the second one, note that<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-1%2Fa%29%5E2+=+a%5E2-2%2B1%2Fa%5E2 ALIGN=MIDDLE  ALT=\"%28a-1%2Fa%29%5E2+=+a%5E2-2%2B1%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "so that one will be easy after you have solved the first one.  And for the third of these, you can get the answer in a similar fashion by squaring your answer for the first one. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );