Question

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

Answer 1

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

Answer 2

one sec!

Answer 3

Ok! This one's fun.

Answer 4

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

Answer 5

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

Answer 6

\[x^2 -t^2 = (2t-x)^2\]

Answer 7

give it a stab from there

Answer 8

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

Answer 9

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

Answer 10

ahh! yup! You gotta FOIL the right side

Answer 11

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

Answer 12

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?

Answer 13

You got it!

Answer 14

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

Answer 15

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

Answer 16

Thanks!