Q46 Matemática  (IMO Shortlist 1966)

Sejam $a,b,c$ reais e $$f(a,b,c)=\left|\frac{|ba|}{|ab|}+\frac{b+a}{ab}-\frac{2}{c}\right|+\frac{|ba|}{|ab|}+\frac{b+a}{ab}+\frac{2}{c}$$ Prove que $f(a,b,c)=4\max \{\frac{1}{a},\frac{1}{b},\frac{1}{c}\}.$