Lösung 2.3:3e

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K
Zeile 1: Zeile 1:
-
In this case, we see that the left-hand side contains the factor
+
In this case, we see that the left-hand side contains the factor <math>x+3</math>, which we can take out to obtain
-
<math>x+\text{3}</math>, which we can take out to obtain
+
-
 
+
-
 
+
-
<math>\begin{align}
+
-
& \left( x+\text{3} \right)\left( x-1 \right)-\left( x+\text{3} \right)\left( 2x-9 \right)=\left( x+\text{3} \right)\left( \left( x-1 \right)-\left( 2x-9 \right) \right) \\
+
-
& =\left( x+\text{3} \right)\left( x-1-2x+9 \right)=\left( x+\text{3} \right)\left( -x+8 \right). \\
+
-
\end{align}</math>
+
 +
{{Displayed math||<math>\begin{align}
 +
(x+3)(x-1) - (x+3)(2x-9)
 +
&= (x+3)\bigl((x-1)-(2x-9)\bigr)\\[5pt]
 +
&= (x+3)(x-1-2x+9)\\[5pt]
 +
&= (x+3)(-x+8)\,\textrm{.}
 +
\end{align}</math>}}
This rewriting of the equation results in the new equation
This rewriting of the equation results in the new equation
 +
{{Displayed math||<math>(x+3)(-x+8)=0</math>}}
-
<math>\left( x+\text{3} \right)\left( -x+8 \right)=0</math>
+
which has the solutions <math>x=-3</math> and <math>x=8\,</math>.
-
 
+
-
 
+
-
which has the solutions
+
-
<math>x=-\text{3}</math>
+
-
and
+
-
<math>x=\text{8}</math>.
+
-
We check the solution
+
We check the solution <math>x=8</math> by substituting it into the equation,
-
<math>x=\text{8 }</math>
+
-
by substituting it into the equation:
+
-
LHS
+
{{Displayed math||<math>\text{LHS} = (8+3)\cdot (8-1) - (8+3)\cdot (2\cdot 8 - 9) = 11\cdot 7 - 11\cdot 7 = 0 = \textrm{RHS.}</math>}}
-
<math>=\left( 8+3 \right)\centerdot \left( 8-1 \right)-\left( 8+3 \right)\centerdot \left( 2\centerdot 8-9 \right)=11\centerdot 7-11\centerdot 7=0=</math>
+
-
RHS
+

Version vom 08:47, 29. Sep. 2008

In this case, we see that the left-hand side contains the factor \displaystyle x+3, which we can take out to obtain

Vorlage:Displayed math

This rewriting of the equation results in the new equation

Vorlage:Displayed math

which has the solutions \displaystyle x=-3 and \displaystyle x=8\,.

We check the solution \displaystyle x=8 by substituting it into the equation,

Vorlage:Displayed math

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