Solution 2.3:4c - Revision history

Tek at 10:39, 29 September 2008

2008-09-29T10:39:04Z

←Older revision		Revision as of 10:39, 29 September 2008
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-	The equation	+	The equation <math>(x-3)(x-\sqrt{3}\,)=0</math> is a second-degree equation which has <math>x=3</math> and <math>x=\sqrt{3}</math> as roots; when <math>x=3</math>, the first factor is zero and when <math>x=\sqrt{3}</math> the second factor is zero.
-	<math>~~\left~~( x-~~\text{~~3~~} \right~~)~~\left~~( x-\sqrt~~{\text~~{3}} \~~right~~)=0</math>	+
-	is a second-degree equation which has	+
-	<math>x=~~\text{~~3 }</math>	+
-	and	+
-	<math>x=\sqrt~~{\text~~{3}}</math>	+
-	as roots; when	+
-	<math>x=~~\text{~~3 }</math>, the first factor is zero and when	+
-	<math>x=\sqrt~~{\text~~{3}}</math>	+
-	the second factor is zero.	+

-	If we expand the ~~equations~~ left-hand side, we get the equation in standard form,	+	If we expand the equation's left-hand side, we get the equation in standard form,

		+	{{Displayed math\|\|<math>\begin{align}
		+	(x-3)(x-\sqrt{3}\,)
		+	&= x^{2}-\sqrt{3}x-3x+3\sqrt{3}\\[5pt]
		+	&= x^{2}-(3+\sqrt{3}\,)x+3\sqrt{3}=0\,\textrm{.}
		+	\end{align}</math>}}

-	<math>\begin{align}
-	& \left( x-\text{3} \right)\left( x-\sqrt{\text{3}} \right)=x^{2}-\sqrt{\text{3}}x-3x+3\sqrt{\text{3}} \\
-	& =x^{2}-\left( 3+\sqrt{\text{3}} \right)x+3\sqrt{\text{3}}=0 \\
-	\end{align}</math>

		+	Note: the general answer is

-	~~NOTE: the general answer is~~,	+	{{Displayed math\|\|<math>ax^{2}-(3+\sqrt{3}\,)ax+3\sqrt{3}a=0\,,</math>}}

-		+	where <math>a\ne 0</math> is a constant.
-	~~<math>ax^{2}-\left( 3+\sqrt{\text{3}} \right)ax+3\sqrt{\text{3}}a=0</math>~~	+
-		+
-		+
-	where	+
-	<math>a\ne 0</math>	+
-	is a constant.	+

Ian at 09:38, 21 September 2008

2008-09-21T09:38:29Z

←Older revision		Revision as of 09:38, 21 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	The equation
-	<~~center~~> ~~[[Image:2_3_4c~~.~~gif]]~~ </~~center~~>	+	<math>\left( x-\text{3} \right)\left( x-\sqrt{\text{3}} \right)=0</math>
-	{{~~NAVCONTENT_STOP~~}}	+	is a second-degree equation which has
		+	<math>x=\text{3 }</math>
		+	and
		+	<math>x=\sqrt{\text{3}}</math>
		+	as roots; when
		+	<math>x=\text{3 }</math>, the first factor is zero and when
		+	<math>x=\sqrt{\text{3}}</math>
		+	the second factor is zero.
		+
		+	If we expand the equations left-hand side, we get the equation in standard form,
		+
		+
		+	<math>\begin{align}
		+	& \left( x-\text{3} \right)\left( x-\sqrt{\text{3}} \right)=x^{2}-\sqrt{\text{3}}x-3x+3\sqrt{\text{3}} \\
		+	& =x^{2}-\left( 3+\sqrt{\text{3}} \right)x+3\sqrt{\text{3}}=0 \\
		+	\end{align}</math>
		+
		+
		+	NOTE: the general answer is,
		+
		+
		+	<math>ax^{2}-\left( 3+\sqrt{\text{3}} \right)ax+3\sqrt{\text{3}}a=0</math>
		+
		+
		+	where
		+	<math>a\ne 0</math>
		+	is a constant.

Tekbot: Lösning 2.3:4c moved to Solution 2.3:4c: Robot: moved page

2008-09-09T09:00:43Z

Lösning 2.3:4c moved to Solution 2.3:4c: Robot: moved page

←Older revision

Revision as of 09:00, 9 September 2008

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

2008-08-21T06:47:29Z

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

←Older revision		Revision as of 06:47, 21 August 2008
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2008-04-01T10:09:22Z

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