Bunuel wrote:
Official Solution:
If \(x\) and \(y\) are negative numbers, what is the value of \(\frac{\sqrt{x^2}}{x}-\sqrt{-y*|y|}\)?
A. \(1+y\)
B. \(1-y\)
C. \(-1-y\)
D. \(y-1\)
E. \(x-y\)
Note that \(\sqrt{a^2}=|a|\). Next, since \(x \lt 0\) and \(y \lt 0\) then \(|x|=-x\) and \(|y|=-y\).
So, \(\frac{\sqrt{x^2}}{x}-\sqrt{-y*|y|}=\frac{|x|}{x}-\sqrt{(-y)*(-y)}=\frac{-x}{x}-\sqrt{y^2}=-1-|y|=-1+y\)
Answer: D
For anyone that picked C over D, like I did, plug in numbers:
Let X = -2, and Let Y = -3 (also let -X = 2, and Let -Y = 3)
You end up with:
\(\frac{2}{-2} - \sqrt{3*3}\) = \(-1 - 3\)
Now look back - 3 = -Y, so 1- -Y = 1 + Y. D'oh!