Solution 2.3:5b - Revision history

Tek at 11:10, 29 September 2008

Tek — Mon, 29 Sep 2008 11:10:53 GMT

←Older revision		Revision as of 11:10, 29 September 2008
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-	Instead of randomly trying different values of	+	Instead of randomly trying different values of ''x'', it is better investigate the second-degree expression by completing the square,
-	~~<math>~~x~~</math>~~	+
-	, it is better investigate the second-degree expression by completing the square:	+

		+	{{Displayed math\|\|<math>\begin{align}
		+	4x^{2} - 28x + 48
		+	&= 4(x^{2} - 7x + 12)\\[5pt]
		+	&= 4\bigl((x-\tfrac{7}{2})^{2} - (\tfrac{7}{2})^{2} + 12\bigr)\\[5pt]
		+	&= 4\bigl((x-\tfrac{7}{2})^{2} - \tfrac{49}{4} + \tfrac{48}{4}\bigr)\\[5pt]
		+	&= 4\bigl((x-\tfrac{7}{2})^{2} - \tfrac{1}{4}\bigr)\\[5pt]
		+	&= 4\bigl(x - \tfrac{7}{2}\bigr)^{2}-1\,\textrm{.}
		+	\end{align}</math>}}

-	<math>~~\begin{align}~~	+	In the expression in which the square has been completed, we see that if, e.g.
-	~~& 4x^{2}-28x+48=4\left(~~ x~~^{2}-7x+12 \right)~~=~~4\left( \left( x-\frac{~~7}{2~~} \right)^{2}-\left( \frac{7}{2} \right)^{2}+12 \right) \\~~	+	<math>x=7/2</math>, then the whole expression is negative and equal to -1.
-	~~& =4\left( \left( x-\frac{7}{2} \right)^{2}-\frac{49}{4}+\frac{48}{4} \right)=4\left( \left( x-\frac{7}{2} \right)^{2}-\frac{1}{4} \right)=4\left( x-\frac{7}{2} \right)^{2}-1. \\~~	+
-	~~\end{align}~~</math>	+


-	~~In the expression in which the square has been completed, we see that if, e.g.~~	+	Note: All values of ''x'' between 3 and 4 give a negative value for the expression.
-	~~<math>x={7}/{2}\;</math>, then the whole expression is negative and equal to~~	+
-	~~<math>-\text{1}</math>.~~	+
-		+
-	~~NOTE~~: All values of	+
-	~~<math>~~x~~</math>~~	+
-	between	+
-	~~<math>\text{~~3~~}</math>~~	+
-	and	+
-	~~<math>\text{~~4~~}</math>~~	+
-	give a negative value for the expression.	+

Ian at 09:57, 21 September 2008

Ian — Sun, 21 Sep 2008 09:57:11 GMT

←Older revision		Revision as of 09:57, 21 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	Instead of randomly trying different values of
-	<~~center~~> ~~[[Image:2_3_5b~~.~~gif]]~~ </~~center~~>	+	<math>x</math>
-	{{~~NAVCONTENT_STOP~~}}	+	, it is better investigate the second-degree expression by completing the square:
		+
		+
		+	<math>\begin{align}
		+	& 4x^{2}-28x+48=4\left( x^{2}-7x+12 \right)=4\left( \left( x-\frac{7}{2} \right)^{2}-\left( \frac{7}{2} \right)^{2}+12 \right) \\
		+	& =4\left( \left( x-\frac{7}{2} \right)^{2}-\frac{49}{4}+\frac{48}{4} \right)=4\left( \left( x-\frac{7}{2} \right)^{2}-\frac{1}{4} \right)=4\left( x-\frac{7}{2} \right)^{2}-1. \\
		+	\end{align}</math>
		+
		+
		+	In the expression in which the square has been completed, we see that if, e.g.
		+	<math>x={7}/{2}\;</math>, then the whole expression is negative and equal to
		+	<math>-\text{1}</math>.
		+
		+	NOTE: All values of
		+	<math>x</math>
		+	between
		+	<math>\text{3}</math>
		+	and
		+	<math>\text{4}</math>
		+	give a negative value for the expression.

Tekbot: Lösning 2.3:5b moved to Solution 2.3:5b: Robot: moved page

Tekbot — Tue, 09 Sep 2008 09:01:23 GMT

Lösning 2.3:5b moved to Solution 2.3:5b: Robot: moved page

←Older revision

Revision as of 09:01, 9 September 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

Tekbot — Thu, 21 Aug 2008 06:47:49 GMT

Robot: Automated text replacement (-[[Bild: +[[Image:)

←Older revision		Revision as of 06:47, 21 August 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:2_3_5b.gif]] </center>	+	<center> [[Image:2_3_5b.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Oskar: Ny sida: {{NAVCONTENT_START}} Bild:2_3_5b.gif {{NAVCONTENT_STOP}}

Oskar — Tue, 01 Apr 2008 10:10:56 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:2_3_5b.gif </center> {{NAVCONTENT_STOP}}

New page

{{NAVCONTENT_START}}
<center> [[Bild:2_3_5b.gif]] </center>
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