document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996546>Question 996546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.) Solve: sqrt x-3 = sqrt 2 - sqrt x for x\r<BR>\n" );
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document.write( "2.) Solve: sqrt 2y-6 = 3-y for y\r<BR>\n" );
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document.write( "3.) Solve: 5 - sqrt 20x + 4 greater than equal to -3 \r<BR>\n" );
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document.write( "4.) The solution to sqrt 3x + 4 greater than equal to 2 is x greater than or equal to 0 (true or false) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614951 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=614951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Solve: sqrt x-3 = sqrt 2 - sqrt x for x <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Square both sides. You will get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+3 ALIGN=MIDDLE  ALT=\"x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%282%29%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%29%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%282%29%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%29%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%282%29%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%29%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Square both sides again:\r<BR>\n" );
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document.write( "25 = 8x.\r<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F8 ALIGN=MIDDLE  ALT=\"25%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<U>Check</U>: &nbsp;Left side is &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%2F8-3%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2F8-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2825-24%29%2F8%29 ALIGN=MIDDLE  ALT=\"sqrt%28%2825-24%29%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2F8%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282%2Asqrt%282%29%29 ALIGN=MIDDLE  ALT=\"1%2F%282%2Asqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Right side is &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%2F8%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F%282%2Asqrt%282%29%29%29 ALIGN=MIDDLE  ALT=\"%285%2F%282%2Asqrt%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-5%29%2F%282%2Asqrt%282%29%29 ALIGN=MIDDLE  ALT=\"%284-5%29%2F%282%2Asqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%282%2Asqrt%282%29%29 ALIGN=MIDDLE  ALT=\"-1%2F%282%2Asqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The results for the left side and the right side are different.\r<BR>\n" );
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document.write( "It means that the original equation has no solutions. &nbsp;(The solution that we obtained is the solution to the equation \r<BR>\n" );
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document.write( "with the squared left and right sides of the original equation, &nbsp;but it doesn't satisfy the original equation. \r<BR>\n" );
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document.write( "Again, &nbsp;it means that the original equation has no solutions).\r<BR>\n" );
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document.write( "The plots in the Figure below confirm this conclusion.\r<BR>\n" );
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document.write( "<TABLE >\n" );
document.write( " \r\n" );
document.write( "  <TR>\r\n" );
document.write( "  <TD > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-5.5%2C+5.5%2C+-5.5%2C+5.5%2C%0D%0A++++++++++sqrt%28x-3%29%2C%0D%0A++++++++++sqrt%282%29-sqrt%28x%29%2C%0D%0A++++++++++sqrt%28x-3%29+-+%28sqrt%282%29-sqrt%28x%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Plots: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;(red); &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29-sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29-sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;(green); &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29+-+%28sqrt%282%29-sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29+-+%28sqrt%282%29-sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;(blue).\r<BR>\n" );
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document.write( "  </TD>\r\n" );
document.write( "  </TR>\r\n" );
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document.write( "</TABLE><BR>\n" );
document.write( " </SPAN>\n" );
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