Răspuns:
a) x = 8 ; y = 4 ; z = 2
b) x = 12 ; y = 6 ; z = 3
c) x = 16; y = 8 ; z = 4
Explicație pas cu pas:
[tex]2x = 4y = 8z = k = > x = \frac{k}{2} ; y = \frac{k}{4} ; z = \frac{k}{8}[/tex]
a)
[tex]x + y + z = 14[/tex]
[tex]\frac{k}{2} + \frac{k}{4} + \frac{k}{8} = 14[/tex]
[tex]\frac{4k+2k+k}{8} = 14[/tex]
[tex]7k = 112[/tex]
[tex]k = 16[/tex]
[tex]x = \frac{16}{2} = 8[/tex]
[tex]y = \frac{16}{4} = 4[/tex]
[tex]z = \frac{16}{8} = 2[/tex]
b)
[tex]x+y+z=21[/tex]
[tex]\frac{k}{2} +\frac{k}{4} + \frac{k}{8} = 21[/tex]
[tex]\frac{4k+2k+k}{8} = 21[/tex]
[tex]7k = 168[/tex]
[tex]k = 24[/tex]
[tex]x = \frac{24}{2} = 12[/tex]
[tex]y = \frac{24}{4} = 6[/tex]
[tex]z = \frac{24}{8} = 3[/tex]
c)
[tex]x+y+z=28[/tex]
[tex]\frac{k}{2} + \frac{k}{4} +\frac{k}{8} = 28[/tex]
[tex]\frac{4k+2k+k}{8} = 28[/tex]
[tex]7k = 224[/tex]
[tex]k = 32[/tex]
[tex]x = \frac{32}{2} = 16[/tex]
[tex]y = \frac{32}{4} = 8[/tex]
[tex]z = \frac{32}{8} = 4[/tex]
