Question 1
Let positive $a , b , c , d$ satisfy $abcd = 1$. Prove $a ) \left(ac + bd\right) \left(ad + bc\right) \ge \left(a + b\right) ( c + d$); $b ) \frac{1}{a \left(1 + b\right)} + \frac{1}{b \left(1 + c\right)} + \frac{1}{c \left(1 + d\right)} + \frac{1}{d \left(1 + a\right)} \ge 2$.