อสมการ+เรขาคณิต

[ฟินิกซ์เหินฟ้า]

1.Let $ABCD$ be a rhombus with $BAD=60^\circ $. $S$ and $R$ are chosen inside $ABD$ and $DBC$ such that $SBR=RDS=60^\circ$. Prove that $SR^2 \geq AS \cdot CR$

2.Given is triangle $ABC$. Let $K$ be a point on $AB$, $L$ be a point on $BC$ and $M$ on $KL$. Prove that the inequality $\sqrt[3]{[ABC]}\geq \sqrt[3]{[AKM]}+\sqrt[3]{[MLC]}$, where $[XYZ]$ denotes the area of triangle $XYZ$, holds.

3.Let $a,b,c,d$ positive real numbers and $a+b+c+d=1$. Prove that

$\displaystyle \sum{\left(\frac{a}{b}-\frac{1-b}{1-a} \right)}\geq 0$