G4.1 Let $P$ be a real number. If $\sqrt{3}-2 P+\sqrt{1-2 P}=2$, find the value of $P$.
$\begin{array}{l}(\sqrt{3-2 P})^{2}=(2-\sqrt{1-2 P})^{2} \\ 3-2 P=4-4 \sqrt{1-2 P}+1-2 P \\ 4 \sqrt{1-2 P}=2 \\ 4(1-2 P)=1 \\ P=\frac{3}{8}\end{array}$