document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=449686>Question 449686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the sum of two numbers is 4 and the product of the numbers is 7, find the sum of the squares of the reciprocals of these numbers.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #309320 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=309320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose the numbers are a,b with a+b = 4 and ab = 7. We wish to find\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{a^2} + \frac{1}{b^2}\">.\r<BR>\n" );
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document.write( "This is equal to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{b^2 + a^2}{a^2b^2}\">.\r<BR>\n" );
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document.write( "Right away, we know that since ab = 7, then a^2*b^2 = 49. We can find a^2 + b^2 by squaring a+b:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (a+b)^2 = 4^2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a^2 + 2ab + b^2 = 16\">\r<BR>\n" );
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document.write( "However we know that ab = 7, 2ab = 14, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a^2 + 14 + b^2 = 16 \Rightarrow a^2 + b^2 = 2\">\r<BR>\n" );
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document.write( "We substitute into our desired expression to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{a^2} + \frac{1}{b^2} = \frac{a^2 + b^2}{a^2b^2} = \frac{2}{49}\">. </SPAN>\n" );
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