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Lösung 2.3:1c

Aus Online Mathematik Brückenkurs 1

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As always when completing the square, we focus on the quadratic and linear terms
As always when completing the square, we focus on the quadratic and linear terms
-
<math>2x-x^{2}</math>
+
<math>2x-x^{2}</math>, which we also can write as
-
, which we also can write as
+
<math>-\left( x^{2}-2x \right)</math>
<math>-\left( x^{2}-2x \right)</math>
. If we neglect the minus sign, we can complete square of the expression
. If we neglect the minus sign, we can complete square of the expression

Version vom 11:20, 12. Sep. 2008

As always when completing the square, we focus on the quadratic and linear terms 2x−x2, which we also can write as −x2−2x  . If we neglect the minus sign, we can complete square of the expression 2x−x2 by using the formula


x2−ax=x−2a2−2a2 


and we obtain


x2−2x=x−222−222=x−12−1 


This means that


5+2x−x2=5−x2−2x=5−x−12−1=5−x−12+1=6−x−12


A quick check shows that we have completed the square correctly.:


6−x−12=6−x2−2x+1=6−x2+2x−1=5+2x−x2

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.3:1c“