Question

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Answer 1

Explicação passo-a-passo:

3)

a) 3x²-2x-8=0

a=3

b=-2

c=-8

∆=b²-4ac

∆=(-2)²-4×3×-8

∆=4+96

∆=100

-b±√∆/2a

2±√100/2×3

2±10/6

x¹=2+10/6=12/6=>2

x²=2-10/6=-8/6(÷2)=>-4/3

b) -2x²+3x+5=0

a=-2

b=3

c=5

∆=b²-4ac

∆=3²-4×-2×5

∆=9+40

∆=49

-b±√∆/2a

-3±√49/2×-2

-3±7/-4

x¹=-3+7/-4=4/-4=>-1

x²=-3-7/-4=-10/-4(-1)=10/4(÷2)=>5/2

c) x²-8x+12=0

a=1

b=-8

c=12

∆=b²-4ac

∆=(-8)²-4×1×12

∆=64-48

∆=16

-b±√∆/2a

8±√16/2×1

8±4/2

x¹=8+4/2=12/2=>6

x²=8-4/2=4/2=>2

d) x²-5x+6=0

a=1

b=-5

c=6

∆=b²-4ac

∆=(-5)²-4×1×6

∆=25-24

∆=1

-b±√∆/2a

5±√1/2×1

5±1/2

x¹=5+1/2=6/2=>3

x²=5-1/2=4/2=>2

4) {x+y=1

{x-2y=1

{x+y=1

{x=1+2y

x+y=1

1+2y+y=1

1+3y=1

3y=1-1

3y=0

y=0/3

y=0

x+y=1

x+0=1

x=1-0

x=1

Opção B

5)

{5x-2y=1

{2x+y=4

{5x-2y=1

{y=4-2x

5x-2y=1

5x-2(4-2x)=1

5x-8+4x=1

5x+4x-8=1

9x=1+8

9x=9

x=9/9

x=1

5x-2y=1

5×1-2y=1

5-2y=1

-2y=1-5

-2y=-4(-1)

2y=4

y=4/2

y=2

Opção C