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

[alee]

B is between A and C. If AB = 6x, BC = x^2, and AC = 27, find the values of x

 

[jonboy]

It would help if you draw diagrams on these types of problems. So your's should look something like this:

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 $\displaystyle 3$.