Lösung 2.3:1a
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
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If we consider the rule | If we consider the rule | ||
| - | {{ | + | {{Abgesetzte Formel||<math>(x-a)^{2} = x^{2}-2ax+a^{2}</math>}} |
and move <math>a^{2}</math> over to the left-hand side, we obtain the formula | and move <math>a^{2}</math> over to the left-hand side, we obtain the formula | ||
| - | {{ | + | {{Abgesetzte Formel||<math>(x-a)^{2}-a^{2} = x^{2}-2ax\,\textrm{.}</math>}} |
With the help of this formula, we can rewrite (complete the square of) a mixed expression <math>x^{2}-2ax</math> to a obtain a quadratic expression, <math>(x-a)^{2}-a^{2}</math>. | With the help of this formula, we can rewrite (complete the square of) a mixed expression <math>x^{2}-2ax</math> to a obtain a quadratic expression, <math>(x-a)^{2}-a^{2}</math>. | ||
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The expression <math>x^{2}-2x</math> corresponds to <math>a=1</math> in the formula above and thus | The expression <math>x^{2}-2x</math> corresponds to <math>a=1</math> in the formula above and thus | ||
| - | {{ | + | {{Abgesetzte Formel||<math>x^{2}-2x = (x-1)^{2}-1\,\textrm{.}</math>}} |
Version vom 08:30, 22. Okt. 2008
If we consider the rule
| \displaystyle (x-a)^{2} = x^{2}-2ax+a^{2} |
and move \displaystyle a^{2} over to the left-hand side, we obtain the formula
| \displaystyle (x-a)^{2}-a^{2} = x^{2}-2ax\,\textrm{.} |
With the help of this formula, we can rewrite (complete the square of) a mixed expression \displaystyle x^{2}-2ax to a obtain a quadratic expression, \displaystyle (x-a)^{2}-a^{2}.
The expression \displaystyle x^{2}-2x corresponds to \displaystyle a=1 in the formula above and thus
| \displaystyle x^{2}-2x = (x-1)^{2}-1\,\textrm{.} |
