Question

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Resolva as equações do 2ºgrau em |R:
a)x(x+9)+(x+9)=0
b)3x-2+7x(3x-2)=0
d)3(x-1)-6x=2-2x(x-3)
e)(x+1)(x-1)=2x

Answer 1

a)
x(x+9)+(x+9)=0
x²+9x+x+9=0
x²+10x+9=0

Δ=10²-4(9)
Δ=199-36
Δ=64

x=(-b±√Δ)/2a
x=(-10±√64)/2

x'=(-10+8)/2=-2/2=-1

x"=(-10-8)/2=-18/2=-9

S={-9,-1}


b)
3x-2+7x(3x-2)=0
3x-2+21x²-14x=0
21x²-11x-2=0

Δ=(-11)²-4(21)(-2)
Δ=121+168
Δ=289

x=[-(-11)±√289]/2(21)=(11±17)/42

x'=(11+17)/42=28/42=2/3

x"=(11-17)/42=-6/42=-1/7

S={-1/7,2/3}


d)
3(x-1)-6x=2-2x(x-3)
3x-3-6x=2-2x²+6x
2x²-9x-5=0

Δ=(-9)²-4(2)(-5)
Δ=81+40
Δ=121

x=[-(9)±√121]/2(2)

x=(9±11)/4

x'=(9+11)/4=20/4=5

x""=(9-11)/4=-2/4=-1/2

S={-1/2,5}


e)
(x+1)(x-1)=2x
x²-1=2x
x²-2x-1=0

Δ=(-2)²-4(-1)
Δ=4+4
Δ=8
√Δ=√8=√2³=±2√2

x=[-(-2)±2√2)/2
x=(2±2√2)/2
x=2(1±√2)/2
x=1±√2

x'=1+√2

x"=1-√2