document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1524>Question 1524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello I am having problems solving this quadratic equation by using the quadratic formula, could you please help?\r<BR>\n" );
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document.write( "x<sup>4</sup> - 6x<sup>2</sup> + 5 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face = \"courier new\" size = 2>Hello I am having problems solving this quadratic equation by using the<BR>\n" );
document.write( "quadratic formula, could you please help? x<sup>4</sup>-6x<sup>2</sup>+5=0<BR>\n" );
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document.write( "Yours is not a quadratic equation, but a fourth-degree equation.  A quadratic<BR>\n" );
document.write( "equation must contain no term in a variable higher than 2.  However if a<BR>\n" );
document.write( "trinomial in descending order set equal to zero is such that the variable part<BR>\n" );
document.write( "of the first term is the square of the variable part of the middle term, then<BR>\n" );
document.write( "we can convert the equation into a quadratic equation by making a<BR>\n" );
document.write( "substitution.  <BR>\n" );
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document.write( "x<sup>4</sup> - 6x<sup>2</sup> + 5 = 0 is such an equation because the variable part of the first<BR>\n" );
document.write( "term is x<sup>4</sup>, which is the square of the variable part of the second equation, x<sup>2</sup><BR>\n" );
document.write( "so we let some other letter, say u, represent the variable part of the second<BR>\n" );
document.write( "term.  That is, we let<BR>\n" );
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document.write( "x<sup>2</sup> = u<BR>\n" );
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document.write( "then we square both sides of that and get<BR>\n" );
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document.write( "x<sup>4</sup> = u<sup>2</sup>  <BR>\n" );
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document.write( "So<BR>\n" );
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document.write( "x<sup>4</sup> - 6x<sup>2</sup> + 5 = 0<BR>\n" );
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document.write( "converts to the quadratic equation: <BR>\n" );
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document.write( "u<sup>2</sup> - 6u + 5 = 0<BR>\n" );
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document.write( "Then we factor the left side as<BR>\n" );
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document.write( "(u - 5)(u - 1) = 0<BR>\n" );
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document.write( "Then we set each factor = 0,<BR>\n" );
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document.write( "u - 5 = 0, which gives u = 5<BR>\n" );
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document.write( "u - 1 = 0, which gives u = 1<BR>\n" );
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document.write( "But the object is not to find u, but to find x, so we<BR>\n" );
document.write( "replace u by x<sup>2</sup> in each case: <BR>\n" );
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document.write( "u = 5 so<BR>\n" );
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document.write( "x<sup>2</sup> = 5<BR>\n" );
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document.write( "Taking square roots of both sides we get<BR>\n" );
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document.write( "x = ±<font face = \"symbol\">Ö</font>5<BR>\n" );
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document.write( "Also<BR>\n" );
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document.write( "u = 1 so <BR>\n" );
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document.write( "x<sup>2</sup> = 1<BR>\n" );
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document.write( "Taking square roots of both sides we get<BR>\n" );
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document.write( "x = ±1<BR>\n" );
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document.write( "So there are four answers: x = <font face = \"symbol\">Ö</font>5, -<font face = \"symbol\">Ö</font>5, 1, and -1<BR>\n" );
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document.write( "Edwin<BR>\n" );
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