Question

1.Verificati care din elementele lui E este solutie a ecuatiei indicate:a)2(x+1)=2x+2,E={0;1;2;3};b)4x+1=2;E={1/2;1/3;1/4;1/5}c)(x-2)(x-3)=0;E={0;2;3;4};d)5x+2=3;E={1/2;1/3;1/4;1/5};2.Rezolvati in Q ecuatiile: x-3/4=1/3;1 1/2+x=2 1/3;2 1/5:x=22/10;2 1/2x+0,5=5,6;1,5x+1/5=3,75;2,(6)-1/2=1/3;1/5x+2/5=2/4

Answer 1

a)2(x+1)=2x+2,E={0;1;2;3};
2x+2=2x+2
x=0, solutie este doar 0 care∈ multimii E

b)4x+1=2;E={1/2;1/3;1/4;1/5}
4x=2-1
4x=1
x=1/4
deci deoarece x=1/4, solutie este doar 1/4 care ∈ multimii E

c)(x-2)(x-3)=0;E={0;2;3;4
x²-3x-2x+6=0
x²-5x+6=0
Δ=b²-4ac=25-24=1
x₁=(-b+√Δ)/2a=(5+1)/2=3
x₂=(-b-√Δ)/2a=(5-1)/2=2

x₁=3 si x₂=2 sunt solutiiambele  ∈ multimii E

d)5x+2=3;E={1/2;1/3;1/4;1/5};
5x=3-2
5x=1
x=1/5  care ∈ multimii E

2.Rezolvati in Q ecuatiile: x-3/4=1/3;1 1/2+x=2 1/3;2 1/5:x=22/10;2 1/2x+0,5=5,6;1,5x+1/5=3,75;2,(6)-1/2=1/3;1/5x+2/5=2/4

x-3/4=1/3
x=1/3+3/4
12x/12=(4+9)/12
12x=13
x=13/12

1 1/2+x=2 1/3, 1 1/2=3/2   si 2 1/3=7/3  deci 3/2+x=7/3 aducem la acelasi numitor comun
9+6x=14
6x=14-9
x=5/6


1/2x+0,5=5,6
x/2+5/10=56/10
5x+5=56
5x=56-5
x=51/5


1/5x+2/5=2/4
4x+8=10
4x=10-8
4x=2
x=1/2


1,5x+1/5=3,75;
150x/100+20/100+375/100
150x=(375-20)
150x=350⇒x=7/3