Lösung 2.3:4c

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K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
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If we expand the equation's left-hand side, we get the equation in standard form,
If we expand the equation's left-hand side, we get the equation in standard form,
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{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
(x-3)(x-\sqrt{3}\,)
(x-3)(x-\sqrt{3}\,)
&= x^{2}-\sqrt{3}x-3x+3\sqrt{3}\\[5pt]
&= x^{2}-\sqrt{3}x-3x+3\sqrt{3}\\[5pt]
Zeile 12: Zeile 12:
Note: the general answer is
Note: the general answer is
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{{Displayed math||<math>ax^{2}-(3+\sqrt{3}\,)ax+3\sqrt{3}a=0\,,</math>}}
+
{{Abgesetzte Formel||<math>ax^{2}-(3+\sqrt{3}\,)ax+3\sqrt{3}a=0\,,</math>}}
where <math>a\ne 0</math> is a constant.
where <math>a\ne 0</math> is a constant.

Version vom 08:33, 22. Okt. 2008

The equation \displaystyle (x-3)(x-\sqrt{3}\,)=0 is a second-degree equation which has \displaystyle x=3 and \displaystyle x=\sqrt{3} as roots; when \displaystyle x=3, the first factor is zero and when \displaystyle x=\sqrt{3} the second factor is zero.

If we expand the equation's left-hand side, we get the equation in standard form,

\displaystyle \begin{align}

(x-3)(x-\sqrt{3}\,) &= x^{2}-\sqrt{3}x-3x+3\sqrt{3}\\[5pt] &= x^{2}-(3+\sqrt{3}\,)x+3\sqrt{3}=0\,\textrm{.} \end{align}


Note: the general answer is

\displaystyle ax^{2}-(3+\sqrt{3}\,)ax+3\sqrt{3}a=0\,,

where \displaystyle a\ne 0 is a constant.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.3:4c“