document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199848>Question 1199848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that x and y are integers and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288sqrt%2811%29%2B27%29+=+y-sqrt%28x-2y%29 ALIGN=MIDDLE  ALT=\"sqrt%288sqrt%2811%29%2B27%29+=+y-sqrt%28x-2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%5Ex ALIGN=MIDDLE  ALT=\"-y%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833829 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%2Asqrt%2811%29%2B27%29+=+a%2Bb%2Asqrt%28c%29 ALIGN=MIDDLE  ALT=\"sqrt%288%2Asqrt%2811%29%2B27%29+=+a%2Bb%2Asqrt%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a,b,c are integers and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+%3E=+0 ALIGN=MIDDLE  ALT=\"c+%3E=+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=%28sqrt%288%2Asqrt%2811%29%2B27%29%29%5E2+=+%28a%2Bb%2Asqrt%28c%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%288%2Asqrt%2811%29%2B27%29%29%5E2+=+%28a%2Bb%2Asqrt%28c%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=8%2Asqrt%2811%29%2B27+=+a%5E2%2B2ab%2Asqrt%28c%29%2Bb%5E2%2Ac ALIGN=MIDDLE  ALT=\"8%2Asqrt%2811%29%2B27+=+a%5E2%2B2ab%2Asqrt%28c%29%2Bb%5E2%2Ac\"   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=27%2B8%2Asqrt%2811%29+=+%28a%5E2%2Bb%5E2%2Ac%29%2B2ab%2Asqrt%28c%29 ALIGN=MIDDLE  ALT=\"27%2B8%2Asqrt%2811%29+=+%28a%5E2%2Bb%5E2%2Ac%29%2B2ab%2Asqrt%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equate corresponding terms to form this system of equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2827+=+a%5E2%2Bb%5E2c%2C8+=+2ab%2C11+=+c%29 ALIGN=MIDDLE  ALT=\"system%2827+=+a%5E2%2Bb%5E2c%2C8+=+2ab%2C11+=+c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use c = 11 and we get this slightly reduced system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2827+=+a%5E2%2B11b%5E2%2C8+=+2ab%29 ALIGN=MIDDLE  ALT=\"system%2827+=+a%5E2%2B11b%5E2%2C8+=+2ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which turns into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2827+=+a%5E2%2B11b%5E2%2C4+=+ab%29 ALIGN=MIDDLE  ALT=\"system%2827+=+a%5E2%2B11b%5E2%2C4+=+ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Through a bit of trial and error, or the substitution method, you should find these solutions<BR>\n" );
document.write( "a = 4<BR>\n" );
document.write( "b = 1\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%2Asqrt%2811%29%2B27%29+=+a%2Bb%2Asqrt%28c%29 ALIGN=MIDDLE  ALT=\"sqrt%288%2Asqrt%2811%29%2B27%29+=+a%2Bb%2Asqrt%28c%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=sqrt%288%2Asqrt%2811%29%2B27%29+=+4%2B1%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%288%2Asqrt%2811%29%2B27%29+=+4%2B1%2Asqrt%2811%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=sqrt%288%2Asqrt%2811%29%2B27%29+=+4%2Bsqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%288%2Asqrt%2811%29%2B27%29+=+4%2Bsqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ... can be verified using WolframAlpha\r<BR>\n" );
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document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%2Asqrt%2811%29%2B27%29+=+y-sqrt%28x-2y%29 ALIGN=MIDDLE  ALT=\"sqrt%288%2Asqrt%2811%29%2B27%29+=+y-sqrt%28x-2y%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=4%2Bsqrt%2811%29+=+y-sqrt%28x-2y%29 ALIGN=MIDDLE  ALT=\"4%2Bsqrt%2811%29+=+y-sqrt%28x-2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "At first things seem fine.<BR>\n" );
document.write( "The 4 and y match up to show y = 4<BR>\n" );
document.write( "But the square root terms do not match up fully.<BR>\n" );
document.write( "The left hand side (LHS) has a positive square root, while the right hand side (RHS) has the square root as negative. <BR>\n" );
document.write( "This is a contradiction that you'll need to ask your teacher about for further clarification.\r<BR>\n" );
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document.write( "If we ignored the positive and negative discrepancy, then we can equate radicands, plug in y = 4 and solve for x.<BR>\n" );
document.write( "11 = x-2y<BR>\n" );
document.write( "11 = x-2*4<BR>\n" );
document.write( "11 = x-8<BR>\n" );
document.write( "x = 11-8<BR>\n" );
document.write( "x = 19\r<BR>\n" );
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document.write( "But as mentioned before, we run into a contradiction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Bsqrt%2811%29+=+y-sqrt%28x-2y%29 ALIGN=MIDDLE  ALT=\"4%2Bsqrt%2811%29+=+y-sqrt%28x-2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Bsqrt%2811%29+=+4-sqrt%2819-2%2A4%29 ALIGN=MIDDLE  ALT=\"4%2Bsqrt%2811%29+=+4-sqrt%2819-2%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Bsqrt%2811%29+=+4-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"4%2Bsqrt%2811%29+=+4-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.316625+=+0.683375 ALIGN=MIDDLE  ALT=\"7.316625+=+0.683375\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It's possible your teacher made a typo somewhere.<BR>\n" );
document.write( "I would ask them for clarification.\r<BR>\n" );
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document.write( "The tutor Edwin McCravy reached a similar conclusion in the link below.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Radicals/Radicals.faq.question.1151181.html\">https://www.algebra.com/algebra/homework/Radicals/Radicals.faq.question.1151181.html</a><BR>\n" );
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