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Lösung 3.3:3a

Aus Online Mathematik Brückenkurs 2

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When we complete the square of the second degree expression, <math>z^2+2z+3</math>, we start with the forumla
When we complete the square of the second degree expression, <math>z^2+2z+3</math>, we start with the forumla
-
{{Displayed math||<math>(z+a)^2 = z^2+2az+a^2</math>}}
+
{{Abgesetzte Formel||<math>(z+a)^2 = z^2+2az+a^2</math>}}
which we write as
which we write as
-
{{Displayed math||<math>(z+a)^2-a^2 = z^2+2az</math>}}
+
{{Abgesetzte Formel||<math>(z+a)^2-a^2 = z^2+2az</math>}}
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
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
-
{{Displayed math||<math>\underline{z^2+2z\vphantom{()}}+3 = \underline{(z+1)^2-1^2}+3 = (z+1)^2 + 2\,\textrm{.}</math>}}
+
{{Abgesetzte Formel||<math>\underline{z^2+2z\vphantom{()}}+3 = \underline{(z+1)^2-1^2}+3 = (z+1)^2 + 2\,\textrm{.}</math>}}
The underlined terms show the actual completion of the square.
The underlined terms show the actual completion of the square.

Version vom 13:12, 10. Mär. 2009

When we complete the square of the second degree expression, z2+2z+3, we start with the forumla

(z+a)2=z2+2az+a2

which we write as

(z+a)2−a2=z2+2az

and adapt the constant to be a=1 so that the terms z2+2z are equal to z2+2az, and therefore can be written as (z+1)2−12. The whole calculation becomes

z2+2z+3=(z+1)2−12+3=(z+1)2+2.

The underlined terms show the actual completion of the square.

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.3:3a“