Question

Exercițiul 1 si 2 va rog frumos....

Answer 1

     Ex:1
a) x²+x-2=0
1. a+b+c=1+1-2=0
2. solutii sunt: x1=-2; x2=1/2
Δ=1²-4*1*(-2)=1+8=9
x₁=(-1-3)/2=-2;   x₂=(-1+2)/2=1/2
b) x²-3x+2=0
1. a+b+c=1-3+2=0
2. solutiile sunt: x1=1; x2=2
Δ=9-8=1
x₁=(3-1)/2=1;   x₂=(3+1)/2=2
c) 2x²-5x+3=0
1. a+b+c=2-5+3=0
2. Solutiile sunt:x1=1;   x2=3/2
Δ= 25-24=1
x₁=(5-1)/4=1;    x₂=(5+1)/4= 3/2
d) 5x²-7x+2=0
1. a+b+c=5-7+2=0
2. Solutiile sunt x1= 2/5;   x2=1
Δ=49-40=49
x1=(7-3)/10=4/10=2/5;  x₂=(7+3)/10=10/10=1
Tabelul 2:
x²+5x+4=0
1. a-b+c=1-5+4=0
2. Solutiile sunt: x1=-4;   x2=-1
Δ=25-16=9
x₁=(-5-3)/2=-8/2=-4;  x₂=(-5+3)/2=-2/2=-1
3x²-7x-10=0
1. a-b+c=3+7=10=0
2. Solutiile sunt: x1=-1;  x2=10/3
Δ= 49+120=169
x₁=(7-13)/6=-6/6=-1;    x₂=(7+13)/6=20/6=10/3
-9x²-4x+5=0
1. a-b+c=-9+4+5=0
2. Solutiile sunt: x1=5/9;   x2=-1
Δ=16+180=196
x₁=(4-14)/-18=10/18=5/9;  x₂=(4+14)/-18=18/-18=-1
13x²+6x-7=0
1. a-b+c=13-6-7=0
2. solutiile sunt: x1=-1;  x2=7/13
Δ= 36+364=400
x₁=(-6-20)/26=-26/26=-1;  x₂=(-6+20)/26=14/26=7/13
Formulele ajutatoare: Δ=b²-4*a*c;
                  x₁=(-b-√Δ)/2a;  x₂=(-b+√Δ)/2a

Ex:2
Daca a+b+c=0, atunci x₁=(-b-√Δ)2a; x₂=(-b+√Δ)2a
Daca a-b+c=0, atunci x₁=(b-√Δ)/2a; x₂=(b+√Δ)/2a