document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993287>Question 993287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what values of \"a\" is the distance between P(a, 3) and Q(6, 2a) greater than 29?<BR>\n" );
document.write( " (Enter your answer using interval notation.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #613184 by </B><A HREF=/tutors/aboutme.mpl?userid=anand429><B>anand429(138)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=anand429><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=anand429><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=613184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distance between P(a,3) and Q(6,2a) is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%286-a%29%5E2+%2B+%282a-3%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%286-a%29%5E2+%2B+%282a-3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2-12a%2B36+%2B+4a%5E2-12a%2B9%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2-12a%2B36+%2B+4a%5E2-12a%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285a%5E2-24a%2B45%29 ALIGN=MIDDLE  ALT=\"sqrt%285a%5E2-24a%2B45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For this distance to be greater than 29;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285a%5E2-24a%2B45%29+%3E+29 ALIGN=MIDDLE  ALT=\"sqrt%285a%5E2-24a%2B45%29+%3E+29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a%5E2-24a%2B45+%3E+841 ALIGN=MIDDLE  ALT=\"5a%5E2-24a%2B45+%3E+841\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a%5E2-24a-796+%3E+0 ALIGN=MIDDLE  ALT=\"5a%5E2-24a-796+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving the quadratic we get roots as -10.44 and 15.24<BR>\n" );
document.write( "Since coefficient of a^2 is positive, the graph is opening upwards<BR>\n" );
document.write( "So the value of this quadratic is negative between these two roots.\r<BR>\n" );
document.write( "\n" );
document.write( "So the required value of a for the quadratic to be positive, is <BR>\n" );
document.write( "All values of a except [-10.44,15.24] range.<BR>\n" );
document.write( " </SPAN>\n" );
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