Lösung 2.3:1c
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
K |
|||
| Zeile 2: | Zeile 2: | ||
<math>2x-x^{2}</math>, which we also can write as <math>-(x^{2}-2x)</math>. If we neglect the minus sign, we can complete square of the expression <math>2x-x^{2}</math> by using the formula | <math>2x-x^{2}</math>, which we also can write as <math>-(x^{2}-2x)</math>. If we neglect the minus sign, we can complete square of the expression <math>2x-x^{2}</math> by using the formula | ||
| - | {{Displayed math||<math>x^{2}-ax = \ | + | {{Displayed math||<math>x^{2}-ax = \Bigl(x-\frac{a}{2}\Bigr)^{2} - \Bigl(\frac{a}{2}\Bigr)^{2}</math>}} |
and we obtain | and we obtain | ||
| - | {{Displayed math||<math>x^{2}-2x = \ | + | {{Displayed math||<math>x^{2}-2x = \Bigl(x-\frac{2}{2}\Bigr)^{2} - \Bigl(\frac{2}{2}\Bigr)^{2} = (x-1)^{2}-1\,\textrm{.}</math>}} |
This means that | This means that | ||
Version vom 14:08, 26. Sep. 2008
As always when completing the square, we focus on the quadratic and linear terms \displaystyle 2x-x^{2}, which we also can write as \displaystyle -(x^{2}-2x). If we neglect the minus sign, we can complete square of the expression \displaystyle 2x-x^{2} by using the formula
and we obtain
This means that
A quick check shows that we have completed the square correctly
