document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1004388>Question 1004388</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bsqrt%28x%29=2 ALIGN=MIDDLE  ALT=\"x%5E2%2Bsqrt%28x%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I know x=1 but I want to know the procedure. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620891 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=620891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Without any computation, x = 1 *has* to be the only real solution because the functions x^2 and sqrt(x) are strictly increasing when x >= 0 (note: if x < 0, then the LHS is non-real). Because x = 1 is a solution, it must be the only real solution.\r<BR>\n" );
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document.write( "Assuming complex-valued square roots, you can solve by isolating sqrt(x) and squaring:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \sqrt{x} = 2 - x^2\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large x = (2 - x^2)^2 = 4 - 4x^2 + x^4\">\r<BR>\n" );
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document.write( "And so on. </SPAN>\n" );
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