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 2.2:2c

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 2.2:2c moved to Solution 2.2:2c: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
We can simplify the left-hand side in the equation by expanding the squares using the squaring rule:
-
<center> [[Image:2_2_2c.gif]] </center>
+
 
-
{{NAVCONTENT_STOP}}
+
 
 +
<math>\begin{align}
 +
& \left( x+3 \right)^{2}-\left( x-5 \right)^{2}=\left( x^{2}+2\centerdot 3x+3^{2} \right)-\left( x^{2}-2\centerdot 5x+5^{2} \right) \\
 +
& =x^{2}+6x+9-x^{2}+10x-25=16x-16 \\
 +
\end{align}</math>
 +
 
 +
 
 +
Thus, the equation is
 +
 
 +
 
 +
<math>16x-16=6x+4</math>
 +
 
 +
 
 +
Now, move all "
 +
<math>x</math>
 +
"s to the left-hand side (subtract
 +
<math>6x</math>
 +
from both sides) and the constants to the right-hand side (add
 +
<math>16</math>
 +
to both sides)
 +
 
 +
 
 +
<math>\begin{align}
 +
& 16x-6x=4+16 \\
 +
& 10x=20 \\
 +
\end{align}</math>
 +
 
 +
 
 +
Divide both sides by
 +
<math>10</math>
 +
to get the answer
 +
 
 +
 
 +
<math>x=\frac{20}{10}=2</math>
 +
 
 +
 
 +
Finally, we check that
 +
<math>x=2</math>
 +
satisfies the equation in the exercise:
 +
 
 +
LHS =
 +
<math>\left( 2+3 \right)^{2}-\left( 2-5 \right)^{2}=5^{2}-\left( -3 \right)^{2}=25-9=16</math>
 +
 
 +
 
 +
RHS =
 +
<math>6\centerdot 2+4=12+4=16</math>

Revision as of 12:58, 17 September 2008

We can simplify the left-hand side in the equation by expanding the squares using the squaring rule:


x+32−x−52=x2+23x+32−x2−25x+52=x2+6x+9−x2+10x−25=16x−16 


Thus, the equation is


16x−16=6x+4


Now, move all " x "s to the left-hand side (subtract 6x from both sides) and the constants to the right-hand side (add 16 to both sides)


16x−6x=4+1610x=20


Divide both sides by 10 to get the answer


x=1020=2


Finally, we check that x=2 satisfies the equation in the exercise:

LHS = 2+32−2−52=52−−32=25−9=16 


RHS = 62+4=12+4=16

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_2.2:2c"