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Lösung 2.3:2f

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
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K
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
Zeile 1: Zeile 1:
We divide both sides by 3 and complete the square on the left-hand side,
We divide both sides by 3 and complete the square on the left-hand side,
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{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
x^{2}-\frac{10}{3}x+\frac{8}{3}
x^{2}-\frac{10}{3}x+\frac{8}{3}
&= \Bigl(x-\frac{5}{3}\Bigr)^{2} - \Bigl(\frac{5}{3}\Bigr)^{2} + \frac{8}{3}\\[5pt]
&= \Bigl(x-\frac{5}{3}\Bigr)^{2} - \Bigl(\frac{5}{3}\Bigr)^{2} + \frac{8}{3}\\[5pt]
Zeile 10: Zeile 10:
The equation then becomes
The equation then becomes
-
{{Displayed math||<math>\left( x-\frac{5}{3} \right)^{2}=\frac{1}{9}\,\textrm{,}</math>}}
+
{{Abgesetzte Formel||<math>\left( x-\frac{5}{3} \right)^{2}=\frac{1}{9}\,\textrm{,}</math>}}
and taking the square root gives the solutions as
and taking the square root gives the solutions as

Version vom 08:32, 22. Okt. 2008

We divide both sides by 3 and complete the square on the left-hand side,

x2−310x+38=x−352−352+38=x−352−925+924=x−352−91.

The equation then becomes

x−352=91, 

and taking the square root gives the solutions as

  • x−35=91=31  i.e. x=35+31=36=2,
  • x−35=−91=−31  i.e. x=35−31=34.

Check:

  • x = 4/3:  LHS=3342−1034+8=3916−340+383=0=RHS, 
  • x = 2:  LHS=322−102+8=12−20+8=0=RHS.
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.3:2f“