document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1022705>Question 1022705</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me out my problem is:<BR>\n" );
document.write( "If a+2b=9 and ab=7 than what is the value of aČ+4b?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638322 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a + 2b = 9 and ab = 7 than what is the value of a^2 + 4b?\r<BR>\n" );
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document.write( "you have a + 2b = 9 and you have ab = 7.\r<BR>\n" );
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document.write( "solve for a in ab = 7 to get a = 7/b.\r<BR>\n" );
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document.write( "a + 2b = 9 becomes 7/b + 2b = 9 after you replace a with 7/b.\r<BR>\n" );
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document.write( "your equation to solve is now 7/b + 2b = 9.\r<BR>\n" );
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document.write( "multiply both sides of that equation by b to get 7 + 2b^2 = 9b.\r<BR>\n" );
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document.write( "subtract 9b from both sides of the equation and reorder the terms in descending order to get 2b^2 - 9b + 7 = 0\r<BR>\n" );
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document.write( "factor that quadratic to get (2b-7) * (b-1) = 0\r<BR>\n" );
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document.write( "solve for b to get b = 7/2 or b = 1.\r<BR>\n" );
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document.write( "when b = 7/2, a + 2b = 9 becomes a + 7 = 9 which becomes a = 2.\r<BR>\n" );
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document.write( "when b = 1, a + 2b = 9 becomes a + 2 = 9 which becomes a = 7.\r<BR>\n" );
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document.write( "you have two possibilities.\r<BR>\n" );
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document.write( "a = 2 and b = 7/2.\r<BR>\n" );
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document.write( "a = 7 and b = 1.\r<BR>\n" );
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document.write( "when a = 2 and b = 7/2, a + 2b = 9 becomes 2 + 7 = 9 which becomes 9 = 9 which is true.\r<BR>\n" );
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document.write( "when a = 2 and b = 7/2 ab = 7 becomes 2 * 7/2 = 7 which becomes 7 = 7 which is true.\r<BR>\n" );
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document.write( "when a = 7 and b = 1, a + 2b = 9 becomes 7 + 2 = 9 which becomes 9 = 9 which is true.\r<BR>\n" );
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document.write( "when a = 7 and b = 1, ab = 7 becomes 7 * 1 = 7 which becomes 7 = 7 which is true.\r<BR>\n" );
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document.write( "the above 4 equations confirm the solutions are correct so far.\r<BR>\n" );
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document.write( "so we have two pairs of solutions in the form of (a,b).\r<BR>\n" );
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document.write( "the are (2,7/2) and (7,1).\r<BR>\n" );
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document.write( "now we look at a^2 + 4b.\r<BR>\n" );
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document.write( "when a = 2 and b = 7/2, a^2 + 4b = 4 + 14 = 18.\r<BR>\n" );
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document.write( "when a = 7 and b = 1, a^2 + 4b = 49 + 4 = 53.\r<BR>\n" );
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document.write( "you have 2 solutions.\r<BR>\n" );
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document.write( "a^2 + 4b = 18 when a = 2 and b = 7/2.\r<BR>\n" );
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document.write( "a^2 + 4b = 53 when a = 7 and b = 1.\r<BR>\n" );
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