Question 4
The quadrilateral $ABCD$ has the following properties:
(i) $AB=AD+BC$;
(ii) there is a point $P$ inside it at a distance $x$ from the side $CD$ such that $AP=x+AD$ and $BP=x+BC$.
Show that
$$\frac1{\sqrt x}\ge\frac1{\sqrt{AD}}+\frac1{\sqrt{BC}}.$$
(i) $AB=AD+BC$;
(ii) there is a point $P$ inside it at a distance $x$ from the side $CD$ such that $AP=x+AD$ and $BP=x+BC$.
Show that
$$\frac1{\sqrt x}\ge\frac1{\sqrt{AD}}+\frac1{\sqrt{BC}}.$$