Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath

Solution 2.3:1a

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
(Ny sida: {{NAVCONTENT_START}} <center> Bild:2_3_1a.gif </center> {{NAVCONTENT_STOP}})
Current revision (13:22, 26 September 2008) (edit) (undo)
m
 
(3 intermediate revisions not shown.)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
If we consider the rule
-
<center> [[Bild:2_3_1a.gif]] </center>
+
 
-
{{NAVCONTENT_STOP}}
+
{{Displayed math||<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
 +
 
 +
{{Displayed math||<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>.
 +
 
 +
The expression <math>x^{2}-2x</math> corresponds to <math>a=1</math> in the formula above and thus
 +
 
 +
{{Displayed math||<math>x^{2}-2x = (x-1)^{2}-1\,\textrm{.}</math>}}

Current revision

If we consider the rule

(x−a)2=x2−2ax+a2

and move a2 over to the left-hand side, we obtain the formula

(x−a)2−a2=x2−2ax.

With the help of this formula, we can rewrite (complete the square of) a mixed expression x2−2ax to a obtain a quadratic expression, (x−a)2−a2.

The expression x2−2x corresponds to a=1 in the formula above and thus

x2−2x=(x−1)2−1.
Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_2.3:1a"