G1.4 Given that $x$ and $y$ are real numbers and $\left|x-\frac{1}{2}\right|+\sqrt{y^{2}-1}=0$.
Let $p=|x|+|y|$, find the value of $p$.
Reference: 2005 FI4.1, 2006 FI4.2, 2011 FI4.3, 2013 FI1.4, 2015 HG4, 2015 FI1.1 Both $\left|x-\frac{1}{2}\right|$ and $\sqrt{y^{2}-1}$ are non-negative numbers.

The sum of two non-negative numbers $=0$ means each of them is zero
$$
x=\frac{1}{2}, y= \pm 1 ; p=\frac{1}{2}+1=\frac{3}{2}
$$