Question

determinati numerele x y si z invers proportionale cu 3 6 si 9 stiind ca b) x+y+z=42 c) x + y + z=84

va rog repede dau 35 de puncte si coroana.​

Answer 1

Răspuns:

Explicație pas cu pas:

{x ; y ; z} i.p {3 ; 6 ; 9}

3x = 6y = 9z = k, unde k = coeficient de propoționalitate

x = k/3

y = k/6

z = k/9

b)

x + y + z = 42

k/3 + k/6 + k/9 = 42 | × 18

6k + 3k + 2k = 504

11k = 504

k = 504/11

x = 504/11/3 = 504/11 × 1/3 = 504/33 = 168/11

y = 504/11/6 = 504/11 × 1/6 = 504/66 = 84/11

z = 504/11/9 = 504/11 × 1/9 = 504/99 = 56/11

c)

x + y + z = 84

k/3 + k/6 + k/9 = 84 | × 18

6k + 3k + 2k = 1512

11k = 1512

k = 1512/11

x = 1512/11/3 = 1512/11 × 1/3 = 1512/33 = 504/11

y = 1512/11/6 = 1512/11 × 1/6 = 1512/66 = 252/11

z = 1512/11/9 = 1512/11 × 1/9 = 1512/99 = 168/11