document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=765156>Question 765156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Every time I try to solve this equation I come up with no solution, but that answer is incorrect. Help please?<BR>\n" );
document.write( "[(11-x^2)^1/2]-[2/(11-x^2)^1/2]=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #465975 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=465975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [(11-x^2)^1/2]-[2/(11-x^2)^1/2]=1<BR>\n" );
document.write( "let u = [(11-x^2)^1/2] and then we have<BR>\n" );
document.write( "u^2 -2 = u and<BR>\n" );
document.write( "u^2 -u -2 = 0, factor this<BR>\n" );
document.write( "(u-2) * (u+1) = 0, so we have<BR>\n" );
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document.write( "[(11-x^2)^1/2] = 2<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "11 -x^2 = 4<BR>\n" );
document.write( "multiply both sides of = by -1<BR>\n" );
document.write( "x^2 -11 = -4<BR>\n" );
document.write( "x^2 = 7<BR>\n" );
document.write( "x = sqrt(7)<BR>\n" );
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document.write( "[(11-x^2)^1/2] = -1<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "11 -x^2 = 1<BR>\n" );
document.write( "multiply both sides of = by -1<BR>\n" );
document.write( "x^2 -11 = -1<BR>\n" );
document.write( "x^2 = 10<BR>\n" );
document.write( "x = sqrt(10)<BR>\n" );
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document.write( "now we substitute back in original equation to check<BR>\n" );
document.write( "(11 -7)^1/2 - 2 / (11-7)^1/2 = 1<BR>\n" );
document.write( "2 - (2 / 2) = 1<BR>\n" );
document.write( "2 - 1 = 1<BR>\n" );
document.write( "x = sqrt(7)  checks out<BR>\n" );
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document.write( "now for x = sqrt(10)<BR>\n" );
document.write( "(11-10)^1/2 - 2 / (11-10)^1/2 = 1<BR>\n" );
document.write( "1 -2/1 = -1<BR>\n" );
document.write( "this does not check out<BR>\n" );
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document.write( "our answer is x = sqrt(7) = 7^1/2<BR>\n" );
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