Question

1. Un automobil merge cu viteza de 80 km/h . El va parcurge in o ora si 45 minute un numar de ..... km
2. Determinati x∈Z astfel incat 3x+2 supra 2x+1 ∈Z
3. x-1 ; y ;z+1 dp 4 5 7
x+y+z supra 3 = 16 . aflati x y z

Answer 1

Am atasat rezolvarea.

Answer 2

1.  v = 80km/h       t = 1h + 45/60 h = 1,75 h     d = v·t = 80·1,75 = 140km
2.  (3x+2)/(2x+1) ∈ Z ⇔  (2x+1) | (3x+2)
daca   d | (3x+2) ⇒ d | 2(3x+2) = 6x + 4    (1)
  si       d | (2x+1) ⇒ d | 3(2x+1) = 6x + 3    (2)
⇒ d | [(1) - (2) = 1] ⇒ d ∈ {-1;1}
2x+1 = - 1    2x = -2   x = -1
2x + 1 = 1    2x = 0   x = 0 ⇒ x ∈ {-1,0}
3. (x-1)/4 = y/5 = (z+1)/7 = k    x-1 = 4k     x = 4k + 1 ;  y = 5k ;
z+1= 7k   z = 7k - 1
(x+y+z)/3 = 16    x+ y+z = 48    4k+1+5k+7k-1 = 48  16k = 48   k = 3
x = 13;   y = 15 ; z = 20