Resolvas as seguintes equações do 2º grau:
A)
x^2-7x+10=0
B)
4x^2-12x=0
C)
2x^2-18=0
D)
x^2-4x+5=0
E)x^2+8x+16=0
F)
x^2-2x-6=0
G)
(x-2)^2=4-9x
H)
(x-3).(x+4)+8=x
I)x.(x+3)=5x
J)
3x^2-36=0
K)
x^2-18x+45=0
L)x^2-2x-4=0
M)
(x+1).(x-3)=-3
N)
9x^2-4=0
O)
(2x-4^2)=0
Soluções para a tarefa
Resposta:Segue as contas abaixo na explicação
Explicação passo-a-passo:
A) x²-7x+10=0 B) 4x²-12x=0 C)2x²-18=0
Δ=b²-4.a.c Δ=b²-4.a.c Δ=b²-4.a.c
Δ=(-7)²-4.1.(10) Δ=(-12)²-4.4.0 Δ=(-18)²-4.2.0
Δ=49-40 Δ=144+0 Δ=324+0
Δ=9 Δ=144 Δ=324
x=-b ± √Δ/2.a x=-b ± √Δ/2.a x=-b ± √Δ/2.a
x=-(-7) ± √9/2.1 x=-(-12) ± √144/2.4 x=-(-18) ± √324/2.2
x=7 ± 3/2 x=12 ± 12/8 x=18 ±/4
x1=7+3/2 x1=12+12/8 x1=18+18/4
x1=10/2 x1=24/8 x1=36/4
x1=5 x1=3 x1=9
x2=7-3/2 x2=12-12/8 x2=18-18/4
x2=4/2 x2=0/8 x2=0/4
x2=2 x2=0 x2=0
S(5,2) S(3,0) S(9,0)
D)x²-4x+5=0 E)x²+8x+16=0 F)x²-2x-6=0
Δ=b²-4.a.c Δ=b²-4.a.c Δ=b²-4.a.c
Δ=(-4)²-4.1.5 Δ=8²-4.1.16 Δ=(-2)²-4.1.(-6)
Δ=16-20 Δ=64-64 Δ=4+24
Δ=-4(não há solução) Δ=0 Δ=28
x=-b ± √Δ/2.a x=-b ± √Δ/2.a
x=-8 ± √0/2.1 x=-(-2) ± √28/2.1
x=-8 ± 0/2 x=2 ± 2√7/2
x1 e x2=-4 x1 e x2=1 ± 1√7
S(-4,-4) S(1+1√7,1-1√7)
G)(x-2)²=4-9x H)(x-3).(x+4)+8=x I)x.(x+3)=5x
(x-2).(x-2)=4-9x x²+4x-3x-12+8=x x²+3x=5x
x²-2x-2x+4=4-9x x²+x-4=x x²+3x-5x=0
x²-4x+4=4-9x x²+x-4-x=0 x²-2x=0
x²-4x+4-4+9x=0 x²-4=0 x(x-2)=0
x²+5x=0 x= ±√4 x=0
x(x+5) x= ± 2 x-2=0
x=0 S(+2,-2) x=2
x+5=0 S(2,0)
x=-5
S(-5,0)
J) 3x²-36=0 K)x²-18x+45=0 L)x²-2x-4=0
3x²=36 Δ=b²-4.a.c Δ=b²-4.a.c
x²=36/3 Δ=(-18)²-4.1.45 Δ=(-2)²-4.1.(-4)
x²=12 Δ=324-180 Δ=4+16
x= ± √12 Δ=144 Δ=20
x= ± 2√3 x=-b ± √Δ/2.a x=-b ± √Δ/2.a
S(+2√3,-2√3) x=-(-18) ± √144/2.1 x=-(-2) ± √20/2.1
x=18 ± 12/2 x=2 ± 2√5/2
x1=18+12/2 x1 e x2=1 ± 1√5
x1=30/2 S(1+1√5,1-1√5)
x1=15
x2=18-12/2
x2=6/2
x2=3
S(15,3)
M) (x+1).(x-3)=-3 N)9x²-4=0 O)(2x-4²)=0
x²-3x+x-3=-3 9x²=4 2x-16=0
x²-2x-3=-3 x= ± √4/9 2x=16
x²-2x-3+3=0 x= ± 2/3 x=16/2
x²-2x=0 S(+2/3,-2/3) x=8
x.(x-2)=0
x=0
x-2=0
x=2
S(2,0)