Question

Determinaţi numerele x, y şi z invers proporţionale cu numerele 2, 3 şi 4, ştiind că: a)x+y-z=7; b)x+z-y = 10; c) y + z-x = 4.
Repede va rog dau coroana!!!!​

Answer 1

{x,y,z} i.p. {2,3,4}
x •2= y•3= z•4=k
x•2=k, x=k/2
y•3=k, y=k/3
z•4=k, z=k/4

X+y-z=7
k/2+k/3-k/4=7, aducem la acelasi numitor
(6k+4k-3k) /12=7
7k/12=7
7k= 7•12
7k=84
K=84:7
k=12
x=k/2, x=12:2, x=6
Y=k/3, y=12:3, y=4
z=k/4, z=12:4, z=3

6•2=4•3=3•4, 12=12=12

b) x+z-y=10
k/2+k/4-k/3=10
(6k+3k-4/k) / 12 = 10
5k / 12 = 10
5k=10•12
5k=120
k=120:5
k=24
x=k/2, x=12
y=k/3, y=8
z=k/4, z=6

12•2=8•3=6•4, 24=24=24

C) y+z-x=4
k/3+k/4-k/2=4
(4k+3k-6k) / 12 = 4
k/12=4
k=4•12
k=48
x=k/2, x=24
y=k/3, y=16
z=k/4, z=12

24•2=16•3=12•4, 48=48=48