Question

Determina numerele rationale pozitive x,y,z care sunt direct proportionale cu numerele 5,6 si 10, iar 2x + 3y-2z =128.

Answer 1

Uite,ma poti intreba daca nu intelegi

Answer 2

{ x, y, z } d.p { 5, 6, 10 } 
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2x + 3y - 2z = 128
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x / 5 = y / 6 = z / 10 = K

x / 5 = K => x = 5 K
y / 6 = K => y = 6 K
z / 10 = K => z = 10 K

⇒ 2 · 5 K + 3 · 6 K - 2 · 10 K = 128

10 K + 18 K - 20 K = 128

28 K - 20 K = 128

8 K = 128

K = 128 : 8 

K  = 16

a = 16 · 5 = 80

b = 16 · 6 = 96

z = 16 · 10 = 160