document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=353546>Question 353546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP ME TO SOLVE THESE QUESTIONS.............\r<BR>\n" );
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document.write( "Q1.IF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B1%2Fx%5E3=2 ALIGN=MIDDLE  ALT=\"x%5E3%2B1%2Fx%5E3=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then find the value of x+1/x\r<BR>\n" );
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document.write( "Q2.FIND THE VALUE OF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E3%2B%28x-2y%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E3%2B%28x-2y%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Q3.IF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%2Fx%29%2A%28x-1%2Fx%29%2A%28x%5E2%2B1%2Fx%5E2%29%2A%28x%5E4%2B1%2Fx%5E4%29%2A%28x%5E8%2B1%2Fx%5E8%29=3%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .then find the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16 ALIGN=MIDDLE  ALT=\"x%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #252638 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=252638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q1.IF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B1%2Fx%5E3=2 ALIGN=MIDDLE  ALT=\"x%5E3%2B1%2Fx%5E3=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then find the value of x+1/x<BR>\n" );
document.write( "Let's start by eliminating the fraction. Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6+%2B+1+=+2x%5E3 ALIGN=MIDDLE  ALT=\"x%5E6+%2B+1+=+2x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To solve a non-linear equation, we often get one side equal to zero and factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6+-+2x%5E3+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"x%5E6+-+2x%5E3+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving this equation is much easier if we notice that the exponent of 6 is twice the exponent of 3. That makes this equation in quadratic form for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Looking at the expression this way we can, perhaps, see that the expression fits the pattern: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+2ab+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+2ab+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which we know is, in factored form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So you equation factors into:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+1%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+-+1%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By the Zero Product Property we know that this (or any) product is zero <i>only</i> if one of the factors is zero. So:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+1+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving this we get x = 1.<BR>\n" );
document.write( "This makes x + 1/x = 1 + 1/1 = 1 + 1 = 2.<br><BR>\n" );
document.write( "Q2.FIND THE VALUE OF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E3%2B%28x-2y%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E3%2B%28x-2y%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This problem does not make sense. You can't find a value unless you have an equation and this has no equals sign. The only thing you can do with this expression is simplify it. That means cubing (x+y) correctly (Hint: It is <b>not</b> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >!) and then combining like terms, if any.<br><BR>\n" );
document.write( "Q3.IF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%2Fx%29%2A%28x-1%2Fx%29%2A%28x%5E2%2B1%2Fx%5E2%29%2A%28x%5E4%2B1%2Fx%5E4%29%2A%28x%5E8%2B1%2Fx%5E8%29=3%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .then find the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16 ALIGN=MIDDLE  ALT=\"x%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first two factors<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%2Fx%29%2A%28x-1%2Fx%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%2Fx%29%2A%28x-1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > fit the pattern of (a+b)(a-b) which we know from the pattern to be equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So your first two factors are equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+1%2Fx%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+-+1%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. But this and the third factor fit the same pattern again. So the first three factors are equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-+1%2Fx%5E4 ALIGN=MIDDLE  ALT=\"x%5E4+-+1%2Fx%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. But this, combined with the next factor fit the pattern again. And this repeats once more time making the entire left side of the equation equal to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+-+1%2Fx%5E16 ALIGN=MIDDLE  ALT=\"x%5E16+-+1%2Fx%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So now our equation looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+-+1%2Fx%5E16+=+3%2F2 ALIGN=MIDDLE  ALT=\"x%5E16+-+1%2Fx%5E16+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can solve this just like we did problem 1. Get rid of the fraction:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E32+-+1+=+%283%2F2%29x%5E16 ALIGN=MIDDLE  ALT=\"x%5E32+-+1+=+%283%2F2%29x%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Get one side equal to zero:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E32+-+%283%2F2%29x%5E16+-+1+=+0 ALIGN=MIDDLE  ALT=\"x%5E32+-+%283%2F2%29x%5E16+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This, like problem 1, is an equation in \"quadratic form\". This time it is in quadratic form for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16 ALIGN=MIDDLE  ALT=\"x%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This equation, unlike problem 1, does not factor easily. When we can't factor, we resort to the Quadratic Formula. This gives us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+%28-%28-3%2F2%29+%2B-+sqrt%28%28-3%2F2%29%5E2+-+4%281%29%28-1%29%29%29%2F2%281%29 ALIGN=MIDDLE  ALT=\"x%5E16+=+%28-%28-3%2F2%29+%2B-+sqrt%28%28-3%2F2%29%5E2+-+4%281%29%28-1%29%29%29%2F2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+%28-%28-3%2F2%29+%2B-+sqrt%289%2F4+-+4%281%29%28-1%29%29%29%2F2%281%29 ALIGN=MIDDLE  ALT=\"x%5E16+=+%28-%28-3%2F2%29+%2B-+sqrt%289%2F4+-+4%281%29%28-1%29%29%29%2F2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+%283%2F2+%2B-+sqrt%289%2F4+%2B+4%29%29%2F2 ALIGN=MIDDLE  ALT=\"x%5E16+=+%283%2F2+%2B-+sqrt%289%2F4+%2B+4%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+%283%2F2+%2B-+sqrt%289%2F4+%2B+16%2F4%29%29%2F2 ALIGN=MIDDLE  ALT=\"x%5E16+=+%283%2F2+%2B-+sqrt%289%2F4+%2B+16%2F4%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+%283%2F2+%2B-+sqrt%2825%2F4%29%29%2F2 ALIGN=MIDDLE  ALT=\"x%5E16+=+%283%2F2+%2B-+sqrt%2825%2F4%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+%283%2F2+%2B-+5%2F2%29%2F2 ALIGN=MIDDLE  ALT=\"x%5E16+=+%283%2F2+%2B-+5%2F2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In long form this is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+%283%2F2+%2B+5%2F2%29%2F2 ALIGN=MIDDLE  ALT=\"x%5E16+=+%283%2F2+%2B+5%2F2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+%283%2F2+-+5%2F2%29%2F2 ALIGN=MIDDLE  ALT=\"x%5E16+=+%283%2F2+-+5%2F2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looking at the second equation, we see that the fraction will be negative. And since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16 ALIGN=MIDDLE  ALT=\"x%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be equal to a negative number, there will be no solutions to the second equation. So we only have to solve the first equation. we continue by simplifying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+%288%2F2%29%2F2 ALIGN=MIDDLE  ALT=\"x%5E16+=+%288%2F2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+4%2F2 ALIGN=MIDDLE  ALT=\"x%5E16+=+4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E16+=+2 ALIGN=MIDDLE  ALT=\"x%5E16+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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