Stim ca:
[tex]\frac{a}{n} =\frac{b}{m} =\frac{c}{p} =\frac{d}{q} =7[/tex]
Trebuie sa calculam:
[tex]\frac{a+b}{m+n}+\frac{b+c}{m+p}+\frac{c+d}{p+q} + \frac{d+a}{q+n} -17[/tex]
Pornim de la ipoteza:
[tex]\frac{a}{n} =\frac{b}{m} =\frac{c}{p} =\frac{d}{q} =7[/tex]
a=7n
b=7m
c=7p
d=7q
Inlocuim in ce trebuie sa aflam si obtinem:
[tex]\frac{a+b}{m+n}+\frac{b+c}{m+p}+\frac{c+d}{p+q} + \frac{d+a}{q+n} -17\\\\\frac{7n+7m}{m+n}+\frac{7m+7p}{m+p}+\frac{7p+7q}{p+q} + \frac{7q+7n}{q+n} -17[/tex]
Vom da factor comun pe 7 si obtinem:
[tex]\frac{7(m+n)}{m+n}+\frac{7(m+p)}{m+p}+\frac{7(p+q)}{p+q} + \frac{7(q+n)}{q+n} -17[/tex]
Simplificam m+n, m+p, p+q si q+n si obtinem:
7+7+7+7-17=28-17=11
Raspuns: 11
