CGMO 2011 Problem 3

The positive reals $a,b,c,d$ satisfy $abcd=1$ . Prove that $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} + \frac{9}{{a + b + c + d}} \geqslant \frac{{25}}{4}$ .