<p>No it is not impossible, yes I am having trouble with it and most of you will probably find it extremely easy but I would appreciate some guidance. Also, this has probably been answered but I looked and could not find it. </p>
<p>(x^2-t^2) = 2t-x PARENTHESIS INDICATE SQUARE ROOT.</p>
<p>If x and t are positive numbers that satisfy the equation above, what is the value of x/t ?</p>
<p>Once again the x squared and negative t squared are inside a square root sign. I would like to know how to solve it -- I know the answer already -- but the way I solved took way too long and I feel there must be a shorter path. Thanks.</p>
<p>√(x^2 - t^2) = 2t - x **Original Equation<a href=“x%5E2-t%5E2”>/B</a> = (2t-x)^2 **Square both sides<a href=“x%5E2-t%5E2”>/B</a> = 4t^2 + x^2 - 4tx FOIL
0 = 5t^2 -4tx Simplify like terms
0 = t (5t-4x) Factor out a t
0 = 5t-4x Divide by t
5t = 4x</p>
<p>x=5
t=4</p>
<p>Wow it really is that easy; thank you I appreciate it.</p>
<p>0 = t (5t-4x) Factor out a t
0 = 5t-4x Divide by t
5t = 4x</p>
<p>x=5
t=4</p>
<p>Not sure if you can “factor” out a t, since there’s a possibility that it’s 0. But if it was, then x/t would have no definite answer if t was zero. </p>
<p>So that means the zero factor must be “5t-4x”. Just a small thing but that’s my thought process. Good explanation.</p>
<p>If t could equal zero, then there would be a possibility that x/t is nonreal. (dividing by zero) I don’t think there are imaginary solutions on the SAT, and x and t are stated to be positive and therefore real, so it’s fine to factor it out. You’ve got two good explanations already, so I needn’t say more.</p>