Inmultim cele 2 rapoarte
[tex]\frac{a}{b}*\frac{c}{a}=\frac{a}{c}=\frac{2}{5}*\frac{3}{4}=\frac{3}{10}[/tex]
Si vedem si rapoartele inversate ce valori au
[tex]\frac{b}{a}=\frac{5}{2}[/tex]
[tex]\frac{c}{b}=\frac{4}{3}[/tex]
[tex]\frac{c}{a}=\frac{10}{3}[/tex]
Si acum putem sa calculam expresia
[tex]E=\frac{a*a}{b*c}+\frac{b*b}{a*c}+\frac{c*c}{a*b}=\frac{a}{b}*\frac{a}{c}+\frac{b}{a}*\frac{b}{c}+\frac{c}{a}*\frac{c}{b}=\frac{2}{5}*\frac{3}{10}+\frac{5}{2}*\frac{3}{4}+\frac{10}{3}*\frac{4}{3}=\frac{3}{25}+\frac{15}{8}+\frac{40}{9}=\frac{3*8*9}{25*8*9}+\frac{15*9*25}{25*8*9}+\frac{40*25*8}{25*8*9}=\frac{216+3375+8000}{1800}=\frac{11591}{1800}[/tex]
