Solution 2.3:2a - Revision history

Tek at 14:20, 26 September 2008

Tek — Fri, 26 Sep 2008 14:20:06 GMT

←Older revision		Revision as of 14:20, 26 September 2008
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-	We solve the second order equation by combining together the x2- and	+	We solve the second order equation by combining together the ''x''²- and ''x''-terms by completing the square to obtain a quadratic term, and then solve the resulting equation by taking the root.
-	~~<math>~~x~~</math>~~	+
-	-terms by completing the square to obtain a quadratic term, and then solve the resulting equation by taking the root.	+

	By completing the square, the left-hand side becomes		By completing the square, the left-hand side becomes

-		+	{{Displayed math\|\|<math>\underline{x^{2}-4x\vphantom{()}}+3 = \underline{(x-2)^{2}-2^{2}}+3 = (x-2)^{2}-1\,\textrm{,}</math>}}
-	<math>\underline{x^{2}-4x}+3=\underline{~~\left~~( x-2 ~~\right~~)^{2}-2^{2}}+3=~~\left~~( x-2 ~~\right~~)^{2}-1</math>	+
-		+

	where the underlined part on the right-hand side is the actual completed square. The equation can therefore be written as		where the underlined part on the right-hand side is the actual completed square. The equation can therefore be written as

		+	{{Displayed math\|\|<math>(x-2)^{2}-1 = 0</math>}}

-	~~<math>\left( x-2 \right)^{2}-1=0</math>~~	+	which we solve by moving the "1" on the right-hand side and taking the square root. This gives the solutions:
-		+
-		+
-	which we solve by moving the "	+
-	~~<math>~~1~~</math>~~	+
-	" on the right-hand side and taking the square root. This gives the solutions	+
-		+

-	<math>x-2=\sqrt{1}=1</math>	+	:*<math>x-2=\sqrt{1}=1\,,\ </math> i.e. <math>x=2+1=3\,,</math>
-	i.e.	+
-	<math>x=2+1=3~~</math>~~	+
-		+
-		+
-	~~<math>x-2=-~~\~~sqrt{1}=-1</math>~~	+
-	~~i.e.~~	+
-	~~<math>x=2-1=1~~</math>	+

		+	:*<math>x-2=-\sqrt{1}=-1\,,\ </math> i.e. <math>x=2-1=1\,\textrm{.}</math>

-	Because it is easy to make a mistake, we check the answer by substituting
-	<math>x=1</math>
-	and
-	<math>x=3</math>
-	into the original equation.:

		+	Because it is easy to make a mistake, we check the answer by substituting <math>x=1</math> and <math>x=3</math> into the original equation:

-	<math>x=\text{1}~~</math>: LHS~~=	+	:*''x'' = 1: <math>\ \text{LHS} = 1^{2}-4\cdot 1+3 = 1-4+3 = 0 = \text{RHS,}</math>
-	~~<math>~~1^{2}-4\~~centerdot~~ 1+3=1-4+3=0</math>	+
-	~~= RHS~~	+

-	~~<math>~~x=3</math>: LHS=	+	:*''x'' = 3: <math>\ \text{LHS} = 3^{2}-4\cdot 3+3 = 9-12+3 = 0 = \text{RHS.}</math>
-	~~<math>~~3^{2}-4\~~centerdot~~ 3+3=9-12+3=0</math>	+
-	~~= RHS~~	+

Ian at 13:21, 20 September 2008

Ian — Sat, 20 Sep 2008 13:21:17 GMT

←Older revision		Revision as of 13:21, 20 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	We solve the second order equation by combining together the x2- and
-	<~~center~~> ~~[[Image:2_3_2a~~.~~gif]]~~ </~~center~~>	+	<math>x</math>
-	{{~~NAVCONTENT_STOP~~}}	+	-terms by completing the square to obtain a quadratic term, and then solve the resulting equation by taking the root.
		+
		+	By completing the square, the left-hand side becomes
		+
		+
		+	<math>\underline{x^{2}-4x}+3=\underline{\left( x-2 \right)^{2}-2^{2}}+3=\left( x-2 \right)^{2}-1</math>
		+
		+
		+	where the underlined part on the right-hand side is the actual completed square. The equation can therefore be written as
		+
		+
		+	<math>\left( x-2 \right)^{2}-1=0</math>
		+
		+
		+	which we solve by moving the "
		+	<math>1</math>
		+	" on the right-hand side and taking the square root. This gives the solutions
		+
		+
		+	<math>x-2=\sqrt{1}=1</math>
		+	i.e.
		+	<math>x=2+1=3</math>
		+
		+
		+	<math>x-2=-\sqrt{1}=-1</math>
		+	i.e.
		+	<math>x=2-1=1</math>
		+
		+
		+	Because it is easy to make a mistake, we check the answer by substituting
		+	<math>x=1</math>
		+	and
		+	<math>x=3</math>
		+	into the original equation.:
		+
		+
		+	<math>x=\text{1}</math>: LHS=
		+	<math>1^{2}-4\centerdot 1+3=1-4+3=0</math>
		+	= RHS
		+
		+	<math>x=3</math>: LHS=
		+	<math>3^{2}-4\centerdot 3+3=9-12+3=0</math>
		+	= RHS

Tekbot: Lösning 2.3:2a moved to Solution 2.3:2a: Robot: moved page

Tekbot — Tue, 09 Sep 2008 08:56:03 GMT

Lösning 2.3:2a moved to Solution 2.3:2a: Robot: moved page

←Older revision

Revision as of 08:56, 9 September 2008

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

Tekbot — Thu, 21 Aug 2008 06:45:09 GMT

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

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Oskar: Ny sida: {{NAVCONTENT_START}} Bild:2_3_2a.gif {{NAVCONTENT_STOP}}

Oskar — Tue, 01 Apr 2008 09:56:09 GMT

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