From Förberedande kurs i matematik 2

Revision as of 15:06, 16 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 3.3:3a moved to Solution 3.3:3a: Robot: moved page) ← Previous diff		Current revision (13:27, 30 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	When we complete the square of the second degree expression, <math>z^2+2z+3</math>, we start with the forumla
-	<center> [[Image:3_3_3a.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>(z+a)^2 = z^2+2az+a^2</math>}}
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		+	which we write as
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		+	{{Displayed math||<math>(z+a)^2-a^2 = z^2+2az</math>}}
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		+	and adapt the constant to be <math>a=1</math> so that the terms <math>z^2+2z</math> are equal to <math>z^2+2az</math>, and therefore can be written as <math>(z+1)^2-1^2</math>. The whole calculation becomes
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		+	{{Displayed math||<math>\underline{z^2+2z\vphantom{()}}+3 = \underline{(z+1)^2-1^2}+3 = (z+1)^2 + 2\,\textrm{.}</math>}}
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		+	The underlined terms show the actual completion of the square.

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Current revision

When we complete the square of the second degree expression, \displaystyle z^2+2z+3, we start with the forumla

\displaystyle (z+a)^2 = z^2+2az+a^2

which we write as

\displaystyle (z+a)^2-a^2 = z^2+2az

and adapt the constant to be \displaystyle a=1 so that the terms \displaystyle z^2+2z are equal to \displaystyle z^2+2az, and therefore can be written as \displaystyle (z+1)^2-1^2. The whole calculation becomes

\displaystyle \underline{z^2+2z\vphantom{()}}+3 = \underline{(z+1)^2-1^2}+3 = (z+1)^2 + 2\,\textrm{.}

The underlined terms show the actual completion of the square.