Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

Solution 2.3:1b

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m
Current revision (14:07, 26 September 2008) (edit) (undo)
m
 
Line 1: Line 1:
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>\biggl(x+\frac{a}{2}\biggr)^{2} - \biggl(\frac{a}{2}\biggr)^{2}\,\textrm{.}</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.
Line 7: Line 7:
If we use this formula, we obtain
If we use this formula, we obtain
-
{{Displayed math||<math>x^{2}+2x = \biggl(x+\frac{2}{2}\biggr)^{2} - \biggl(\frac{2}{2}\biggr)^{2} = (x+1)^{2}-1</math>}}
+
{{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

Current revision

When we complete the square, it is only the first two terms, x2+2x, that are involved. The general formula for completing the square states that x2+ax equals

x+2a2−2a2. 

Note how the coefficient a in front of the x turns up halved in two places.

If we use this formula, we obtain

x2+2x=x+222−222=(x+1)2−1 

and if we subtract the last "1", we obtain

x2+2x−1=(x+1)2−1−1=(x+1)2−2.

To be completely certain that we have used the correct formula, we can expand the quadratic on the right-hand side,

(x+1)2−2=x2+2x+1−2=x2+2x−1

and see that the relation really holds.

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_2.3:1b"