document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=950712>Question 950712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I need help with these radical equation questions. Thanks in advance :) \r<BR>\n" );
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document.write( "Solve each equation and check for extraneous solutions: \r<BR>\n" );
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document.write( "1. [sqrt(2x^2 - 1)]=x\r<BR>\n" );
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document.write( "A.[sqrt(1/3)] <BR>\n" );
document.write( "B.{-1,1} <BR>\n" );
document.write( "C.{-1/2,1} <BR>\n" );
document.write( "D.1 <BR>\n" );
document.write( "E.0 <BR>\n" );
document.write( "F.none of the above \r<BR>\n" );
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document.write( "2.[sqrt(2x^2 + 5x + 6)]=x\r<BR>\n" );
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document.write( "A.no solution <BR>\n" );
document.write( "B.{-2,-3} <BR>\n" );
document.write( "C.{2,3} <BR>\n" );
document.write( "D.-2 <BR>\n" );
document.write( "E.3 <BR>\n" );
document.write( "F.0\r<BR>\n" );
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document.write( "3. [sqrt(x + 3)] = 2[SQRT(x)]\r<BR>\n" );
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document.write( "A.no real solution <BR>\n" );
document.write( "B.3 <BR>\n" );
document.write( "C.{-3,3} <BR>\n" );
document.write( "D.0 <BR>\n" );
document.write( "E.3/2 <BR>\n" );
document.write( "F.1 \r<BR>\n" );
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document.write( "4.[sqrt(2x^2 + x - 12)] = x\r<BR>\n" );
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document.write( "A.[sqrt(6)] <BR>\n" );
document.write( "B.3 <BR>\n" );
document.write( "C.no solution <BR>\n" );
document.write( "D.[sqrt(12)] <BR>\n" );
document.write( "E.2 <BR>\n" );
document.write( "F.{-2,2} \r<BR>\n" );
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document.write( "5.[sqrt(2x^2 + 6x + 4)] = x + 1\r<BR>\n" );
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document.write( "A.1 <BR>\n" );
document.write( "B.{-3, -1} <BR>\n" );
document.write( "C.{-3/2, -1} <BR>\n" );
document.write( "D.no solution <BR>\n" );
document.write( "E.-1 <BR>\n" );
document.write( "F.-3  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580571 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=580571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%5E2+-1%29%29=x ALIGN=MIDDLE  ALT=\"%28sqrt%282x%5E2+-1%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-1=0 ALIGN=MIDDLE  ALT=\"x%5E2-1=0\"   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=%28x-1%29%28x%2B1%29=0 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "answer is: <BR>\n" );
document.write( "B.{-1,1} \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%28-1%2C-1%2C.12%29%2Ccircle%281%2C1%2C.12%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2C-sqrt%282x%5E2+-1%29%2C+sqrt%282x%5E2+-1%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B+2%29%2B+3%28x+%2B+2%29=0 ALIGN=MIDDLE  ALT=\"x%28x%2B+2%29%2B+3%28x+%2B+2%29=0\"   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=%28x%2B+3%29%28x+%2B+2%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B+3%29%28x+%2B+2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B+3%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B+3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+2%29=0 ALIGN=MIDDLE  ALT=\"%28x+%2B+2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "answer:\r<BR>\n" );
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document.write( "B.{-2,-3} \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%28-2%2C-2%2C.12%29%2Ccircle%28-3%2C-3%2C.12%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2C-sqrt%282x%5E2+%2B+5x+%2B+6%29%2C+sqrt%282x%5E2+%2B+5x+%2B+6%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x+%2B+3%29%29%5E2+=%28+2sqrt%28x%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28x+%2B+3%29%29%5E2+=%28+2sqrt%28x%29%29%5E2\"   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=3+=+3x ALIGN=MIDDLE  ALT=\"3+=+3x\"   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=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "answer:\r<BR>\n" );
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document.write( "F.1 \r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281+%2B+3%29+=+2sqrt%281%29 ALIGN=MIDDLE  ALT=\"sqrt%281+%2B+3%29+=+2sqrt%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29+=+2%2A1 ALIGN=MIDDLE  ALT=\"sqrt%284%29+=+2%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+2 ALIGN=MIDDLE  ALT=\"2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, these lines intersect at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   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;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%281%2C2%2C.12%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28x+%2B+3%29%2C+2%2Asqrt%28x%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-3%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29=0 ALIGN=MIDDLE  ALT=\"%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><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;\" >\r<BR>\n" );
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document.write( "answer is:<BR>\n" );
document.write( "B.3 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%283%2C-3%2C.12%29%2Ccircle%28-4%2C-4%2C.12%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2Csqrt%282x%5E2+%2B+x+-12%29%2C+-sqrt%282x%5E2+%2B+x+-12%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "5.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%5E2+%2B+6x+%2B+4%29%29%5E2+=+%28x+%2B+1%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%282x%5E2+%2B+6x+%2B+4%29%29%5E2+=+%28x+%2B+1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+6x+%2B+4=+x%5E2%2B2x+%2B+1 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+6x+%2B+4=+x%5E2%2B2x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+6x+%2B+4-x%5E2-2x+-+1=0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+6x+%2B+4-x%5E2-2x+-+1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+%2B+3=0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+%2B+3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2Bx%2B+3x+%2B+3=0 ALIGN=MIDDLE  ALT=\"x%5E2+%2Bx%2B+3x+%2B+3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2Bx%29%2B+%283x+%2B+3%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2Bx%29%2B+%283x+%2B+3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x+%2B1%29%2B+3%28x+%2B+1%29=0 ALIGN=MIDDLE  ALT=\"x%28x+%2B1%29%2B+3%28x+%2B+1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B3%29%28x+%2B+1%29=0 ALIGN=MIDDLE  ALT=\"%28x+%2B3%29%28x+%2B+1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solutions:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B3%29=0 ALIGN=MIDDLE  ALT=\"%28x+%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+1%29=0 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "answer:<BR>\n" );
document.write( "B.{-3, -1} \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%28-3%2C-2%2C.12%29%2Ccircle%28-1%2C0%2C.12%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B1%2C-sqrt%282x%5E2+%2B+6x+%2B+4%29%2Csqrt%282x%5E2+%2B+6x+%2B+4%29+%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );