x/6 = 6/x-8 Answer is x = 4 + 2 times the square root of 13, but I don't know how to derive it

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- Jan 22nd 2009, 06:37 PMChuckShow how to solve for x
x/6 = 6/x-8 Answer is x = 4 + 2 times the square root of 13, but I don't know how to derive it

- Jan 22nd 2009, 06:59 PMLast_Singularity
- Jan 22nd 2009, 08:09 PMTKHunny
Gack! "Last" is sleeping on the job.

1) Please don't EVER casually multiply by 'x' wihtout at least considering the consequences. If x = 0, you are in big trouble!

2) Please write more carefully. Remember your Order of Operations. You have not written what you intended. You meant this:

x/6 = 6/(x-8)

Look at this and what you wrote and see the difference.

#1 Notice that x = 8 is no good. Why? No matter what else happens, do NOT believe that x = 8.

Having said that, multiply both sides by 'x-8'. This gives:

Multiply both sides by 6. Why was there no additional consideration this time? We know already that 6 is NOT zero (0).

Now we have:

or

or

And that should be familar and suggest, if nothing else, Completing the Square or the Quadratic Formula. - Jan 22nd 2009, 08:16 PMLast_Singularity
- Jan 22nd 2009, 08:24 PMJhevon