Solution 3.2:4 - Revision history

Tek at 12:42, 1 October 2008

2008-10-01T12:42:13Z

←Older revision		Revision as of 12:42, 1 October 2008
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	Square both sides of the equation so that the root sign disappears,		Square both sides of the equation so that the root sign disappears,

		+	{{Displayed math\|\|<math>1-x = (2-x)^2\quad \Leftrightarrow \quad 1-x = 4-4x+x^2</math>}}

-	~~<math>1~~-~~x=\left( 2-x \right)^{2}\quad \Leftrightarrow \quad 1-x=4-4x+x^{2}</math>~~	+	and then solve the resulting second-order equation by completing the square,

		+	{{Displayed math\|\|<math>\begin{align}
		+	x^{2}-3x+3 &= 0\,,\\[5pt]
		+	\Bigl(x-\frac{3}{2}\Bigr)^{2} - \Bigl(\frac{3}{2}\Bigr)^{2} + 3 &= 0\,,\\[5pt]
		+	\Bigl(x-\frac{3}{2}\Bigr)^{2} - \frac{9}{4} + \frac{12}{4} &= 0\,,\\[5pt]
		+	\Bigl(x-\frac{3}{2}\Bigr)^{2} + \frac{3}{4} &= 0\,\textrm{.}
		+	\end{align}</math>}}

-	~~and then solve the resulting second-order equation by completing the square:~~	+	As can be seen, the second-order equation does not have any solutions (the left-hand side is always greater than or equal to 3/4, regardless of how ''x'' is chosen) so, the original root equation does not have any solutions.
-		+
-		+
-	~~<math>\begin{align}~~	+
-	~~& x^{2}-3x+3=0 \\~~	+
-	~~& \left( x-\frac{3}{2} \right)^{2}-\left( \frac{3}{2} \right)^{2}+3=0 \\~~	+
-	~~& \left( x-\frac{3}{2} \right)^{2}-\frac{9}{4}+\frac{12}{4}=0 \\~~	+
-	~~& \left( x-\frac{3}{2} \right)^{2}+\frac{3}{4}=0 \\~~	+
-	~~\end{align}</math>~~	+
-		+
-		+
-	As can be seen, the second-order equation does not have any solutions (the left-hand side is always greater than or equal to	+
-	~~<math>{~~3}/{4~~}\;</math>~~, regardless of how	+
-	~~<math>~~x~~</math>~~	+
-	is chosen; so, the original root equation does not have any solutions.	+

Ian at 10:37, 25 September 2008

2008-09-25T10:37:05Z

←Older revision		Revision as of 10:37, 25 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	Square both sides of the equation so that the root sign disappears,
-	<~~center~~> ~~[[Image~~:~~3_2_4.gif]]~~ <~~/center~~>	+
-	{{~~NAVCONTENT_STOP~~}}	+
		+	<math>1-x=\left( 2-x \right)^{2}\quad \Leftrightarrow \quad 1-x=4-4x+x^{2}</math>
		+
		+
		+	and then solve the resulting second-order equation by completing the square:
		+
		+
		+	<math>\begin{align}
		+	& x^{2}-3x+3=0 \\
		+	& \left( x-\frac{3}{2} \right)^{2}-\left( \frac{3}{2} \right)^{2}+3=0 \\
		+	& \left( x-\frac{3}{2} \right)^{2}-\frac{9}{4}+\frac{12}{4}=0 \\
		+	& \left( x-\frac{3}{2} \right)^{2}+\frac{3}{4}=0 \\
		+	\end{align}</math>
		+
		+
		+	As can be seen, the second-order equation does not have any solutions (the left-hand side is always greater than or equal to
		+	<math>{3}/{4}\;</math>, regardless of how
		+	<math>x</math>
		+	is chosen; so, the original root equation does not have any solutions.

Tekbot: Lösning 3.2:4 moved to Solution 3.2:4: Robot: moved page

2008-09-09T09:18:23Z

Lösning 3.2:4 moved to Solution 3.2:4: Robot: moved page

←Older revision

Revision as of 09:18, 9 September 2008

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

2008-08-21T06:56:19Z

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

←Older revision		Revision as of 06:56, 21 August 2008
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-	<center> [[~~Bild~~:3_2_4.gif]] </center>	+	<center> [[Image:3_2_4.gif]] </center>
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Oskar: Ny sida: {{NAVCONTENT_START}} Bild:3_2_4.gif {{NAVCONTENT_STOP}}

2008-04-01T15:06:24Z

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