Lösung 3.3:3a
Aus Online Mathematik Brückenkurs 2
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Version vom 10:45, 11. Mär. 2009
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.
