Lösung 2.3:1b
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
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When we complete the square, it is only the first two terms, <math>x^{2}+2x</math>, that are involved. The general formula for completing the square states that <math>x^{2}+ax</math> equals | When we complete the square, it is only the first two terms, <math>x^{2}+2x</math>, that are involved. The general formula for completing the square states that <math>x^{2}+ax</math> equals | ||
| - | {{Displayed math||<math>\ | + | {{Displayed math||<math>\Bigl(x+\frac{a}{2}\Bigr)^{2} - \Bigl(\frac{a}{2}\Bigr)^{2}\,\textrm{.}</math>}} |
Note how the coefficient ''a'' in front of the ''x'' turns up halved in two places. | Note how the coefficient ''a'' in front of the ''x'' turns up halved in two places. | ||
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If we use this formula, we obtain | If we use this formula, 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</math>}} |
and if we subtract the last "1", we obtain | and if we subtract the last "1", we obtain | ||
Version vom 14:07, 26. Sep. 2008
When we complete the square, it is only the first two terms, \displaystyle x^{2}+2x, that are involved. The general formula for completing the square states that \displaystyle x^{2}+ax equals
Note how the coefficient a in front of the x turns up halved in two places.
If we use this formula, we obtain
and if we subtract the last "1", we obtain
To be completely certain that we have used the correct formula, we can expand the quadratic on the right-hand side,
and see that the relation really holds.
