Question

Determinați numerele x, y şi z invers proporţionale cu 2, 4 şi 8, ştiind că:
a) x+y+z=14;
b)x+y+z=21;
c) x+y+z=28.
repede va rog

Answer 1

Răspuns:

Explicație pas cu pas:

a)

2x=4y=8z=K

2x=K

x=K/2

-

4y=K

y=K/4

-

8z=K

z= K/8

⁴⁾K/2+²⁾K/4+K/8= ⁸⁾14

4K+2K+K= 112

7K=112

K=112:7

K= 16

-

x= K/2=16/2=8

y=K/4=16/4=4

z=K/8=16/8=2

-

b)

x=K/4

y=K/2

Z=K/8

¹²⁾K/2+⁶⁾K/4+³⁾K/8=²⁴⁾21

12K+6K+3K=504

21K=504

K=504:21

K= 24

-

x= K/2=24/2=12

y=K/4=24/4=6

z=K/8=24/3=8

-

c)

⁴⁾K/2+²⁾K/4+K/8=⁸⁾28

4K+2K+K=224

7K=224

K=224:7

K=32

-

-

x= K/2=32/2=16

y=K/4=32/4=8

z=K/8=32/8=4