Áp dụng BDT Cauchi với $a = x/căn (1-x); b = y$/căn $(1-y)$
$*\frac{x}{\sqrt{1-x}} + \frac{y}{\sqrt{1-y}} \ge \ 2\sqrt{\frac{xy}{\sqrt{(1-x)(1-y)}}}\ge \ 2\sqrt{\frac{xy}{\sqrt{(1 - (x+y) + xy)}}}$
$\ge \ 2\sqrt{\frac{xy}{\sqrt{xy}}}\ge \ 2\sqrt{{\sqrt{xy}}} (1)$
$*x+y \ge \ 2\sqrt{xy}$
$<=> \frac{x+y}{2} \ge \ \sqrt{xy}$
$<=> \frac{1}{2} \ge \ \sqrt{xy} (2)$
(1), (2) <=>$ P \ge \ 2\sqrt{\frac{1}{2}} \ge \ 2\sqrt{{\sqrt{xy}}}$
<=> min của P là $2\sqrt{\frac{1}{2}}$