Question

Rezolvați în Z ecuațiile:

a) (x-2)²-x²<4(x-1)

b) (x+1)²-(x+3)²≥(x-1)²-(x-2)²

c)8(x+1)-4(x-3) < 3(x+12)

d) (x+2)²-3(x+4)>(x+3)·(x-5)-2

Answer 1

a) (x-2-x)(x-2+x)<4(x-1)
-2(2x-2)-4(x-1)<0
-4x+4-4x+4<0
0<0 imposibil
solutia e multimea vida

b) (x+1-x-3)(x+1+x+3)< 3(x+12)
-2(2x+4)- 3(x+12)< 0
-4x-8-3x-36< 0
-7x< 44
x> -44/7
x≥n-6
x∈ {-6,-5,-4,....}

c) 8x+8-4x+12< 3x+36
4x+ 20-3x-36< 0
x< 16
x∈ {....,-2,-1,0,.....14,15,16} (de la - infinit la 16)

d)x²+4x+4-3x-12>x²-2x-15-2
3x>-9
x>-3
x∈{-2,-1,0,1,2,3,.....}

O zi buna!