Question

Exercițiul 4, vă rog frumos!

Answer 1

$\frac{a}{n} = \frac{ b}{m} = \frac{c}{p} = \frac{d}{q} = 7 = > \\ = > \frac{a}{n} = 7 = > a = 7n \\ \frac{b}{m} = 7 = > b = 7m \\ \frac{c}{p} = 7 = > c = 7p \\ \frac{d}{q} = 7 = > d = 7q$

$\frac{a + b}{n + m} + \frac{b + c}{m + p} + \frac{c + d}{p + q} + \frac{d + a}{q + n} - 17 = \\ \frac{7n +7m }{n + m} + \frac{7m + 7p}{ m+p } + \frac{7p + 7q}{p + q} + \frac{7q + 7n}{q +n } - 17 = \\ \frac{7(n + m)}{n + m} + \frac{7(m + p)}{m + p} + \frac{7( p+ q)}{p + q} + \frac{7( q+n )}{q + n} - 17 = \\ 7 + 7 + 7 + 7 - 17 = 28 - 17 = 11$

${7}^{2} - \frac{a + b + c + d}{n +m+ p+ q} = \\ {7}^{2} - \frac{7n + 7m + 7p + 7q}{n + m + p + q} = \\ {7}^{2} - \frac{7 \times1 }{1} = 49 - 7 = 42$