Question

cum se calculeaza daca x,y,z sunt invers proportinale cu 2,3 si 5 in ecuatia x-y+2z=34? Multumesc!

Answer 1

[ x, y, z ] i. p. [ 2, 3, 5 ]

x / ( 1 / 2 ) = x : 1 / 2 = x · 2 / 1 = 2 x ·

2 x = 3 y = 5 z = k ⇒ x = k / 2; y = k / 3; z = k / 5

x - y + 2 z = 34

k / 2 - k / 3 + 2 · k / 5 = 34

cmmmc al numitorilor ( 2; 3; 5 ) = 2 x 3 x 5 = 30

15 k - 10 k + 12 k = 30 × 34

17 k = 30 × 34 l : 17

k = 30 × 2

k = 60

x = 60 / 2 = 30

y = 60 / 3 = 20

z = 60 / 5 = 12

Verific: 30 - 20 + 2 × 12 = 10 + 24 = 34

Raspuns: x = 30; y = 20 si z = 12