document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=55943>Question 55943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me solve, sqrt(2+4x) + sqrt(3-4x)=3\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38005 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=38005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sqrt(2+4x) + sqrt(3-4x)=3<BR>\n" );
document.write( "Square both sides to get:<BR>\n" );
document.write( "2+4x + 2sqrt[(2+4x)(3-4x)] + 3-4x = 9<BR>\n" );
document.write( "5 + 2sqrt[6+4x-16x^2] = 9<BR>\n" );
document.write( "sqrt[6+4x-16x^2] =2<BR>\n" );
document.write( "Square both sides again:<BR>\n" );
document.write( "6+4x-16x^2= 4<BR>\n" );
document.write( "16x^2-4x-2=0<BR>\n" );
document.write( "(2x-1)(8x+2)=0<BR>\n" );
document.write( "x=1/2 or x=1/4<BR>\n" );
document.write( "Checking these answers in the original problem:<BR>\n" );
document.write( "If x=1/2, sqrt(2+2) + sqrt(3-2)=3<BR>\n" );
document.write( "True<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "If x=1/4, sqrt(2+1) + sqrt(3-1)=3<BR>\n" );
document.write( "False<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "The only solution is x=1/2<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );