Lösung 3.3:3a

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When we complete the square of the second degree expression,
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<center> [[Image:3_3_3a.gif]] </center>
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<math>z^{2}+2z+3</math>
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we start with the squaring rule
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<math>\left( z+a \right)^{2}=z^{2}+2az+a^{2}</math>
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which we write as
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<math>\left( z+a \right)^{2}-a^{2}=z^{2}+2az</math>
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and adapt the constant to be
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<math>a=\text{1 }</math>
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so that the terms
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<math>z^{2}+2z</math>
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are equal to
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<math>z^{2}+2az</math>,, and therefore can be written as
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<math>\left( z+1 \right)^{2}-1^{2}</math>. The whole calculation becomes
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<math>\underline{z^{2}+2z}+3=\underline{\left( z+1 \right)^{2}-1^{2}}+3=\left( z+1 \right)^{2}+2</math>
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The underline terms show the actual completion of the square.

Version vom 08:31, 25. Okt. 2008

When we complete the square of the second degree expression, \displaystyle z^{2}+2z+3 we start with the squaring rule


\displaystyle \left( z+a \right)^{2}=z^{2}+2az+a^{2}


which we write as


\displaystyle \left( z+a \right)^{2}-a^{2}=z^{2}+2az


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


\displaystyle \underline{z^{2}+2z}+3=\underline{\left( z+1 \right)^{2}-1^{2}}+3=\left( z+1 \right)^{2}+2


The underline terms show the actual completion of the square.

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