<p>What is the fastest way to do this question:</p>
<p>Sq root of (x^2-t^2) = 2t-x
If x and t are positive numbers that satisfy the equation above, what is the value of (x/t)?</p>
<p>whoops didn't see sqrt</p>
<p>(sqrt(x^2-t^2))^2=4t^2-4tx+x^2
x^2-t^2=4t^2-4tx+x^2
-5t^2=-4tx
t(-5t)=x(-4t)
x/t=5/4</p>
<p>The fastest way might involve a TI-89, but I think it can be solved manually relatively quick...</p>
<p>sqrt(x^2-t^2) = 2t-x</p>
<p>x^2-t^2 = (2t-x)^2</p>
<p>x^2-t^2 = 4t^2-4tx+x^2
-x^2 -x^2</p>
<p>-t^2 = 4t^2-4tx
+t^2 +t^2</p>
<p>5t^2-4tx = 0</p>
<p>5t^2 = 4tx
divide by t</p>
<p>5t = 4x
x/t = 5/4</p>
<p>solve((x^2-t^2)^(1/2)=2t-x, x)
Answer:
x = 5t/4 or t = 0</p>