Question

determinati nr x y z invers proporționale cu 3, 6 si 9 stiind ca a) x + y + z = 28 b) x + y + z = 42 si c) x + y + z = 84​

Answer 1

Răspuns:

3x = 6y = 9z = k

x = k / 3

y = k / 6

z = k / 9

x + y + z  = k/3 + k/6 + k/9 = (6k + 3k + 2k) / 18 = 11k / 18

a) x + y + z = 28

11k / 18 = 28

k = 28 * 18 / 11

x = 28 * 6 / 11 = 168 / 11

y = 28 * 3 / 11 = 84 / 11

z = 28 * 2 / 11 = 56 / 11

b) x + y + z = 42

11k / 18 = 42

k = 42 * 18 / 11

x = 42 * 6 / 11 = 252 / 11

y = 42 * 3 / 11 = 126 / 11

z = 42 * 2 / 11 = 84 / 11

c) x + y + z = 84

11k / 18 = 84

k = 84 * 18 / 11

x = 84 * 6 / 11 = 504 / 11

y = 84 * 3 / 11 = 252 / 11

z = 84 * 2 / 11 = 168 / 11

Explicație pas cu pas: