Question 2
Let $a,b,c,d$ be positive numbers with $abcd=1$. Prove:
a) $(ac+bd)(ad+bc)\ge(a+b)(c+d)$.
b) $\dfrac1{a(1+b)}+\dfrac1{b(1+c)}+\dfrac1{c(1+d)}+\dfrac1{d(1+a)}\ge2$.
a) $(ac+bd)(ad+bc)\ge(a+b)(c+d)$.
b) $\dfrac1{a(1+b)}+\dfrac1{b(1+c)}+\dfrac1{c(1+d)}+\dfrac1{d(1+a)}\ge2$.