Question

1)escreva na forma normal ax²+bx+c=0 e resolva as equações abaixo:
a)3x²+5x=-x-9+2x²
b)4+y(y-4)=y
c)(2x+1)²=3
d)(2r-1)(r-3)=10
e)3y²+7y-3=5y-3

Answer 1

A) 3x²+5x= -x -9+2x²

3x² -2x²+5x +x+9=0

x²+6x+9=0

Δ= 6²-4(1.9)

Δ=36-36

Δ=0

X= -6/2

X= -3 ( única raiz) ok

B) 4 +y(y-4)=y

4+y²-4y=y

y²-4y-y +4=0

y² -5y+4=0

Δ=(-5)²-4(1.4)

Δ=25-16

Δ=9

X=- +5+-3/2

X=+5+3/2

X,=8/2

X,=4

X,,=5-3/2

X,,=2/2

X,,= 1

C) (2x +1)²=3

(2x)² +1²=3

4x²+1 =3

4x²=3-1

4x²=2

X²=2/4

x²=1/2

√x²=√1/2

x=+-√1/2

D)(2r-1)(r-3)=10

2r² -6r -r +3-10=0

2r²-7r-7=0

Δ=(-7)² -4(2(-7)

Δ=49 +56

Δ=105

R=+7+-√105/2.2

R=+7+-√105/4

R,=7+√105/4

R,,= 7-√105/4

E) 3y² +7y-3=5y-3

3y² +7y -5y -3+3=0

3y²+2y=0

y(3y +2)=0

y,=0

3y +2

3y=-2

y,,= -2/3