document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209228>Question 1209228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = -3x^2 + 15x + 11.  Compute 1/a^2 + 1/b^2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847873 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=847873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+8x+%2B+7+=+-3x%5E2+%2B+15x+%2B+11 ALIGN=MIDDLE  ALT=\"2x%5E2+-+8x+%2B+7+=+-3x%5E2+%2B+15x+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2-23x-4=0 ALIGN=MIDDLE  ALT=\"5x%5E2-23x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "First a slow algebraic method for finding the answer, using the quadratic formula to find the two roots....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%2823%2Bsqrt%2823%5E2-4%285%29%28-4%29%29%29%2F10=%2823%2Bsqrt%28609%29%29%2F10 ALIGN=MIDDLE  ALT=\"a=%2823%2Bsqrt%2823%5E2-4%285%29%28-4%29%29%29%2F10=%2823%2Bsqrt%28609%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%2823-sqrt%2823%5E2-4%285%29%28-4%29%29%29%2F10=%2823-sqrt%28609%29%29%2F10 ALIGN=MIDDLE  ALT=\"b=%2823-sqrt%2823%5E2-4%285%29%28-4%29%29%29%2F10=%2823-sqrt%28609%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa%5E2=100%2F%2823%5E2%2B609%2B46sqrt%28609%29%29=100%2F%281138%2B46sqrt%28609%29%29 ALIGN=MIDDLE  ALT=\"1%2Fa%5E2=100%2F%2823%5E2%2B609%2B46sqrt%28609%29%29=100%2F%281138%2B46sqrt%28609%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fb%5E2=100%2F%2823%5E2%2B609-46sqrt%28609%29%29=100%2F%281138-46sqrt%28609%29%29 ALIGN=MIDDLE  ALT=\"1%2Fb%5E2=100%2F%2823%5E2%2B609-46sqrt%28609%29%29=100%2F%281138-46sqrt%28609%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa%5E2%2B1%2Fb%5E2=100%2F%281138%2B46sqrt%28609%29%29%2B100%2F%281138-46sqrt%28609%29%29 ALIGN=MIDDLE  ALT=\"1%2Fa%5E2%2B1%2Fb%5E2=100%2F%281138%2B46sqrt%28609%29%29%2B100%2F%281138-46sqrt%28609%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa%5E2%2B1%2Fb%5E2=%28100%281138-46sqrt%28609%29%29%2B100%281138%2B46sqrt%28609%29%29%29%2F%281138%5E2-46%5E2%2A609%29=%28100%282276%29%29%2F6400=2276%2F64=569%2F16 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 569/16<br><BR>\n" );
document.write( "And now a MUCH easier solution, using Vieta's Theorem....<br><BR>\n" );
document.write( "Given the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2-23x-4=0 ALIGN=MIDDLE  ALT=\"5x%5E2-23x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Vieta's Theorem tells us<br><BR>\n" );
document.write( "(a+b) = 23/5<BR>\n" );
document.write( "(ab) = -4/5<br><BR>\n" );
document.write( "Rewrite the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa%5E2%2B1%2Fb%5E2 ALIGN=MIDDLE  ALT=\"1%2Fa%5E2%2B1%2Fb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms of (a+b) and (ab).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa%5E2%2B1%2Fb%5E2=%28a%5E2%2Bb%5E2%29%2F%28a%5E2b%5E2%29=%28%28a%5E2%2B2ab%2Bb%5E2%29-2ab%29%2F%28%28ab%29%5E2%29=%28%28a%2Bb%29%5E2-2ab%29%2F%28%28ab%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa%5E2%2B1%2Fb%5E2=%28%2823%2F5%29%5E2-2%28-4%2F5%29%29%2F%28%28-4%2F5%29%5E2%29=%28529%2F25%2B8%2F5%29%2F%2816%2F25%29=%28%28529%2B40%29%2F25%29%2F%2816%2F25%29=569%2F16 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER (again, of course): 569/16<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );