Question

Escreva a equação (x + 2)² = 20 + 4x na forma geral e resolva.

Answer 1

Resposta:

a)x²-4x+3=0 b)x²+x-20=0 c)-15x²-2x+13=0

a=1 a=1 a= -15

b= -4 b=1 b= -2

c=3 c= -20 c=13

Δ=b²-4ac Δ=b²-4ac Δ=b²-4ac

Δ=(-4)²-4*1*3 Δ=1²-4*1*(-20) Δ=(-2)²-4*(-15)*13

Δ=16-4*3 Δ=1-4(-20) Δ=4+60*13

Δ=16-12 Δ=1+80 Δ=4+780

Δ=4 Δ=81 Δ=784

x= -b+-√Δ/2a x= -b+-√Δ/2a x= -b+-√Δ/2a

x= -(-4)+-√4/2*1 x= -1+-√81/2*1 x= -(-2)+-√784/(-15)

x=4+-2/2 x= -1+-9/2 x=2+-28/(-15)

x'=4+2/2 x'= -1+9/2 x'=2+28/(-15)

x'=6/2 x'=8/2 x'=30/(-15)

x'=3 x'=4 x'= -2

x''=4-2/2 x''= -1-9/2 x''=2-28/(-15)

x"=2/2 x''= -10/2 x''= -26/(-15)

x"=1 x"= -5 x''= -26/(-15)

d)4x²-2x²+7x-2x+3=0 e)x²-2x=2x+12

2x²+5x+3=0 x²-2x-2x-12=0

x²-4x-12=0

a=2

b=5

c=3 a=1 b= -4 c=-12

Δ=b²-4ac Δ=b²-4ac

Δ=5²-4*2*3 Δ=(-4)²-4*1*(-12)

Δ=25-24 Δ=16+48

Δ=1 Δ=64

x= -b+-√Δ/2a x= -b+-√Δ/2a

x= -5+-√1/2*2 x= -(-4)+-√64/2*1

x= -5+-1/4 x=4+-8/2

x'= -5+1/4 x'=4+8/2

x'= -4/4 x'=12/2

x'= -1 x'=6

x''= -5-1/4 x''=4-8/2

x''= -6/4 (simplifica por 2) x''= -4/2

x''= -3/2 x''= -2

f)2x²-x+6=4x+4 g)x²-2x-x+2=6

2x²-x-4x+6-4=0 x²-3x+2-6=0

2x²-5x+2=0 x²-3x-4=0

a=2 b= -5 c=2 a=1 b= -3 c= -4

Δ=b²=4ac Δ=b²-4ac

Δ=(-5)²-4*2*2 Δ=(-3)²-4*1*(-4)

Δ=25-16 Δ=9+16

Δ=9 Δ=25

x= -b+-√Δ/2a x= -b+-√Δ/2a

x= -(-5)+-√9/2*2 x= -(-3)+-√25/2*1

x=5+-3/4 x=3+-5/2

x'=5+3/4 x'=3+5/2

x'=8/4 x'=8/2

x'=2 x'=4

x"=5-3/4 x''=3-5/2

x''=2/4 (simplifica por 2) x''=2/2

x''=1/2 x''=1

h)2x²-16x-3x+24=34

2x²+19x+24-34=0

2x²+19x-10=0

a=2 b=19 c= -10

Δ=b²-4ac

Δ=19²-4*2*(-10)

Δ=361-8*(-10)

Δ=361+80

Δ=441

x= -b+-√Δ/2a

x= -19+-√441/2*2

x= -19+-21/4

x'= -19+21/4

x'= 2/4 (simplifica por 2)

x'= 1/2

x''= -19-21/4

x''= -40/4

x''= -10