Find the value of x: If AB = 6x, BC = x^2, and AC = 27, ....

alee

New member
Joined
Aug 15, 2006
Messages
14
B is between A and C. If AB = 6x, BC = x^2, and AC = 27, find the values of x
 
It would help if you draw diagrams on these types of problems. So your's should look something like this:

theringed3.jpg


Hence was can derive:\(\displaystyle \L \;x^2\,+\,6x\,=\,27\\)


Get our equation equal to zero to make a quadratic: \(\displaystyle \L \;x^2\,+\,6x\,-\,27\,=\,0\)


So we need to think: What are two numbers that multiply to give us \(\displaystyle \,-\,27\) and add up to a \(\displaystyle 6\)? That would be \(\displaystyle 9\) and \(\displaystyle \,-\,3\).


So our factors are: \(\displaystyle \L \;(x\.+\,9\,)\,(x\,-\,3)\,=\,0\)


So now we solve both factors: \(\displaystyle \L \;(x\.+\,9\,)\,=\,0\,\to\,x\,=\,-\,9\)


The second factor: \(\displaystyle \L \;(x\,-\,3)\,=\,0\,\to\,x\,=\,3\)


So the values of \(\displaystyle x\) as you can see is \(\displaystyle \,-\,9\) and \(\displaystyle 3\).
 
Top