document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182171>Question 1182171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x,y) = x^2+y^2−4x−8y+30 fonksiyonunun minimum değerinin hangi x ve y noktalarında sağlandığını ve minimum değerin kaç olduğunu analitik çözümleyiniz. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812166 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "f(x,y) = x^2+y^2−4x−8y+30 fonksiyonunun minimum değerinin hangi x ve y noktalarında sağlandığını ve minimum değerin kaç olduğunu analitik çözümleyiniz<br><BR>\n" );
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document.write( "All those \"funny\" letters looked to me like Turkish, and I was right; here is how Google translator interpreted this:<br><BR>\n" );
document.write( "Analyze analytically at which x and y points the minimum value of the function is achieved and what the minimum value is.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Cy%29+=+x%5E2%2By%5E2-4x-8y%2B30 ALIGN=MIDDLE  ALT=\"f%28x%2Cy%29+=+x%5E2%2By%5E2-4x-8y%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Complete the square in x and y:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Cy%29+=+x%5E2-4x%2By%5E2-8y%2B30 ALIGN=MIDDLE  ALT=\"f%28x%2Cy%29+=+x%5E2-4x%2By%5E2-8y%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Cy%29+=+%28%28x%5E2-4x%2B4%29%2B%28y%5E2-8y%2B16%29%2B30%29-4-16 ALIGN=MIDDLE  ALT=\"f%28x%2Cy%29+=+%28%28x%5E2-4x%2B4%29%2B%28y%5E2-8y%2B16%29%2B30%29-4-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Cy%29+=+%28x-2%29%5E2%2B%28y-4%29%5E2%2B10 ALIGN=MIDDLE  ALT=\"f%28x%2Cy%29+=+%28x-2%29%5E2%2B%28y-4%29%5E2%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-4%29%5E2 ALIGN=MIDDLE  ALT=\"%28y-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > both have minimum value 0 -- when x=2 and y=4.<br><BR>\n" );
document.write( "ANSWER: The minimum value, when x=2 and y=4, is 10.<br><BR>\n" );
document.write( " </SPAN>\n" );
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