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		<id>http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?action=history&amp;feed=atom&amp;title=Solution_2.3%3A7c</id>
		<title>Solution 2.3:7c - Revision history</title>
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		<updated>2026-04-08T12:27:01Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.3:7c&amp;diff=5623&amp;oldid=prev</id>
		<title>Tek at 11:58, 29 September 2008</title>
		<link rel="alternate" type="text/html" href="http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.3:7c&amp;diff=5623&amp;oldid=prev"/>
				<updated>2008-09-29T11:58:22Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;

			&lt;table style=&quot;background-color: white; color:black;&quot;&gt;
			&lt;col class='diff-marker' /&gt;
			&lt;col class='diff-content' /&gt;
			&lt;col class='diff-marker' /&gt;
			&lt;col class='diff-content' /&gt;
			&lt;tr&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black;&quot;&gt;←Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black;&quot;&gt;Revision as of 11:58, 29 September 2008&lt;/td&gt;
			&lt;/tr&gt;
		&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;If we complete the square&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;If we complete the square&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;,&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background: #eee; color:black; font-size: smaller;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background: #eee; color:black; font-size: smaller;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;nbsp;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;{{Displayed math||&amp;lt;math&amp;gt;x^{2}+x+1=\Bigl(x+\frac{1}{2}\Bigr)^{2}-\Bigl(\frac{1}{2} \Bigr)^{2}+1 = \Bigl(x+\frac{1}{2}\Bigr)^{2} + \frac{3}{4}\,,&amp;lt;/math&amp;gt;}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background: #eee; color:black; font-size: smaller;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background: #eee; color:black; font-size: smaller;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;del style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;x^{2}+x+1=\left( x+\frac{1}{2} \right)^{2}-\left( \frac{1}{2} \right)^{2}+1=\left( x+\frac{1}{2} \right)^{2}+\frac{3}{4}&amp;lt;/math&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;we see on the right-hand side that we can make the expression arbitrarily large simply by choosing &amp;lt;math&amp;gt;x+\&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;tfrac&lt;/ins&gt;{1}{2}&amp;lt;/math&amp;gt; sufficiently large. Hence, there is no maximum value.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;we see on the right-hand side that we can make the expression arbitrarily large simply by choosing &lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;x+\&lt;del style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;frac&lt;/del&gt;{1}{2}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;sufficiently large. Hence, there is no maximum value.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Tek</name></author>	</entry>

	<entry>
		<id>http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.3:7c&amp;diff=5312&amp;oldid=prev</id>
		<title>Ian at 11:18, 21 September 2008</title>
		<link rel="alternate" type="text/html" href="http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.3:7c&amp;diff=5312&amp;oldid=prev"/>
				<updated>2008-09-21T11:18:33Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;

			&lt;table style=&quot;background-color: white; color:black;&quot;&gt;
			&lt;col class='diff-marker' /&gt;
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			&lt;col class='diff-content' /&gt;
			&lt;tr&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black;&quot;&gt;←Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black;&quot;&gt;Revision as of 11:18, 21 September 2008&lt;/td&gt;
			&lt;/tr&gt;
		&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;{{&lt;del style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;NAVCONTENT_START&lt;/del&gt;}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;If we complete the square&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;del style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;center&amp;gt; [[Image:2_3_7c.gif]] &lt;/del&gt;&amp;lt;/&lt;del style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;center&lt;/del&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;{{&lt;del style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;NAVCONTENT_STOP}&lt;/del&gt;}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;nbsp;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;x^&lt;/ins&gt;{&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;2}+x+1=\left( x+\frac&lt;/ins&gt;{&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/ins&gt;}&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;{2} \right)^{2}-\left( \frac{1}{2} \right)^{2}+1=\left( x+\frac{1}{2} \right)^{2}+\frac{3}{4&lt;/ins&gt;}&amp;lt;/&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/ins&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;nbsp;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;nbsp;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;nbsp;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;we see on the right-hand side that we can make the expression arbitrarily large simply by choosing &lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;nbsp;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;x+\frac&lt;/ins&gt;{&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;1}&lt;/ins&gt;{&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt;}&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;nbsp;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;sufficiently large. Hence, there is no maximum value.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Ian</name></author>	</entry>

	<entry>
		<id>http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.3:7c&amp;diff=3402&amp;oldid=prev</id>
		<title>Tekbot: Lösning 2.3:7c moved to Solution 2.3:7c: Robot: moved page</title>
		<link rel="alternate" type="text/html" href="http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.3:7c&amp;diff=3402&amp;oldid=prev"/>
				<updated>2008-09-09T09:03:43Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;a href=&quot;/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=L%C3%B6sning_2.3:7c&amp;amp;action=edit&quot; class=&quot;new&quot; title=&quot;Lösning 2.3:7c&quot;&gt;Lösning 2.3:7c&lt;/a&gt; moved to &lt;a href=&quot;/wikis/2009/bridgecourse1-ImperialCollege/index.php/Solution_2.3:7c&quot; title=&quot;Solution 2.3:7c&quot;&gt;Solution 2.3:7c&lt;/a&gt;: Robot: moved page&lt;/p&gt;

			&lt;table style=&quot;background-color: white; color:black;&quot;&gt;
			&lt;col class='diff-marker' /&gt;
			&lt;col class='diff-content' /&gt;
			&lt;col class='diff-marker' /&gt;
			&lt;col class='diff-content' /&gt;
			&lt;tr&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black;&quot;&gt;←Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black;&quot;&gt;Revision as of 09:03, 9 September 2008&lt;/td&gt;
			&lt;/tr&gt;
		&lt;/table&gt;</summary>
		<author><name>Tekbot</name></author>	</entry>

	<entry>
		<id>http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.3:7c&amp;diff=2300&amp;oldid=prev</id>
		<title>Tekbot: Robot: Automated text replacement  (-[[Bild: +[[Image:)</title>
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				<updated>2008-08-21T06:48:59Z</updated>
		
		<summary type="html">&lt;p&gt;Robot: Automated text replacement  (-[[Bild: +[[Image:)&lt;/p&gt;

			&lt;table style=&quot;background-color: white; color:black;&quot;&gt;
			&lt;col class='diff-marker' /&gt;
			&lt;col class='diff-content' /&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black;&quot;&gt;←Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black;&quot;&gt;Revision as of 06:48, 21 August 2008&lt;/td&gt;
			&lt;/tr&gt;
		&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background: #eee; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;{{NAVCONTENT_START}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background: #eee; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;{{NAVCONTENT_START}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;-&lt;/td&gt;&lt;td style=&quot;background: #ffa; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&amp;lt;center&amp;gt; [[&lt;del style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;Bild&lt;/del&gt;:2_3_7c.gif]] &amp;lt;/center&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;background: #cfc; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;&amp;lt;center&amp;gt; [[&lt;ins style=&quot;color: red; font-weight: bold; text-decoration: none;&quot;&gt;Image&lt;/ins&gt;:2_3_7c.gif]] &amp;lt;/center&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background: #eee; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;{{NAVCONTENT_STOP}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background: #eee; color:black; font-size: smaller;&quot;&gt;&lt;div&gt;{{NAVCONTENT_STOP}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Tekbot</name></author>	</entry>

	<entry>
		<id>http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.3:7c&amp;diff=792&amp;oldid=prev</id>
		<title>Oskar: Ny sida: {{NAVCONTENT_START}} &lt;center&gt; Bild:2_3_7c.gif &lt;/center&gt; {{NAVCONTENT_STOP}}</title>
		<link rel="alternate" type="text/html" href="http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.3:7c&amp;diff=792&amp;oldid=prev"/>
				<updated>2008-04-01T10:16:57Z</updated>
		
		<summary type="html">&lt;p&gt;Ny sida: {{NAVCONTENT_START}} &amp;lt;center&amp;gt; &lt;a href=&quot;/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Bild:2_3_7c.gif&amp;amp;action=edit&quot; class=&quot;new&quot; title=&quot;Bild:2 3 7c.gif&quot;&gt;Bild:2_3_7c.gif&lt;/a&gt; &amp;lt;/center&amp;gt; {{NAVCONTENT_STOP}}&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{NAVCONTENT_START}}&lt;br /&gt;
&amp;lt;center&amp;gt; [[Bild:2_3_7c.gif]] &amp;lt;/center&amp;gt;&lt;br /&gt;
{{NAVCONTENT_STOP}}&lt;/div&gt;</summary>
		<author><name>Oskar</name></author>	</entry>

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