SAT question:
If x and t are positive numbers that satisfy the equation below, what is the value of x/t?

Question

anonymous · Answer

$$\sqrt{x ^{2}-t ^{2}}=2t-x$$
The answer is apparently 5/4. I would like an explanation.

anonymous · Answer

one sec!

anonymous · Answer

Ok!  This one's fun.

anonymous · Answer

Think right off the bat with problems like this: "I NEED to get each variable on the same side" - so I want the t's on one side and the x's on another

anonymous · Answer

1) Kill the square root: $$\sqrt{x^2 - t^2}^2 = (2t-x)^2$$

anonymous · Answer

$$x^2 -t^2 = (2t-x)^2$$

anonymous · Answer

give it a stab from there

anonymous · Answer

Yes, but when I do that I always end up getting $$5t ^{2}=0$$ because $$x ^{2}-t ^{2}=4t ^{2}+x ^{2}$$

anonymous · Answer

oh... wait. There's another term, duh

anonymous · Answer

ahh!  yup!  You gotta FOIL the right side

anonymous · Answer

so you get x^2 - t^2 = 4t^2 - 4tx + x^2

anonymous · Answer

Oh.. lol. Okay. So then ...  4x = 5t. then 4x/5t = 1, and x/t = 5/4 because you have to multiply by the reciprocal and both sides. Am I right?

anonymous · Answer

You got it!

anonymous · Answer

*facepalm* Let's hope I don't do this on the exam

anonymous · Answer

good job.  I hate missing stuff like that...happens ALL the time! :)

anonymous · Answer

Thanks!