Question

Resolva as equações do 2° grau em R:

A) x(x+1)=30

B) X²+2(X+1)=5

C) 2x(4x-2)-4=0

D) (6x+1)²-16=0

E) (x+1)²=x+7

Answer 1

Resolva as equações do 2° grau em R:

A) x(x+1)=30

x² + 1x = 30 igualar zero OLha o sinal

x² + 1x - 30 = 0

a = 1

b = 1

c = - 30

Δ = b² - 4ac

Δ = (1)² - 4(1)(-30)

Δ = + 1 + 120

Δ = + 121 -------------------> √Δ = 11 ( porque √121 = 11)

se

Δ > 0 ( DUAS raizes diferentes)

(baskara)

(-b + - √Δ)

x = -----------------

2a

x' = - 1 -√121/2(1)

x' = - 1 - 11/2

x' = - 12/2

x' = - 6

e

x'' = - 1 + √121/2(1)

x'' = - 1 + 11/2

x'' = + 10/2

x'' = 5

B) X²+2(X+1)=5

x² + 2x + 2 = 5

x² + 2x + 2 - 5 = 0

x² + 2x - 3 = 0

a = 1

b = 2

c = - 3

Δ = b² - 4ac

Δ = (2)² - 4(1)(-3)

Δ =+ 4 + 12

Δ = + 16 --------------------->√Δ= 4 (√16 = 4)

se

Δ > 0 ( DUAS raizes diferentes)

(baskara)

(-b + - √Δ)

x = -----------------

2a

x' = - 2 - √16/2(1)

x' = - 2 - 4/2

x' = - 6/2

x' = - 3

e

x'' = - 2 + √16/2(1)

x'' = - 2 + 4/2

x'' = + 2/2

x'' = 1

C) 2x(4x-2)-4=0

8x² - 4x - 4 = 0

a = 8

b = - 4

c = - 4

Δ = b² - 4ac

Δ = (-4)² - 4(8)(-4)

Δ = + 16 + 128

Δ = + 144 -----------------------> √Δ = 12 ( √144 = 12)

se

Δ > 0 ( DUAS raizes diferentes)

(baskara)

(-b + - √Δ)

x = -----------------

2a

x' = -(-4) - √144/2(8)

x' = + 4 - 12/16

x' = - 8/16 ( divide AMBOS por 8)

x' = - 1/2

e

x'' = - (-4) + 144/2(8)

x'' = + 4 + 12/16

x'' = 16/16

x'' = 1

D) (6x+1)²-16=0

(6x + 1)(6x + 1) - 16 = 0

(36x² + 6x + 6x + 1) - 16

(36x² + 12x + 1) - 16 = 0

36x² + 12x + 1 - 16 = 0

36x² + 12x - 15 = 0

a = 36

b = 12

c = - 15

Δ = b² - 4ac

Δ = (12)² - 4(36)(-15)

Δ = + 144 + 2160

Δ =+ 2304 -------------------> √Δ= 48 (√2304 = 48)

se

Δ > 0 ( DUAS raizes diferentes)

(baskara)

(-b + - √Δ)

x = -----------------

2a

x' = - 12 - √2304/2(36)

x' = - 12 - 48/72

x' = - 60/72 ( divide AMBOS POR 12)

x' = -5/6

e

x'' = -12 + √2304/2(36)

x'' = - 12 + 48/72

x'' = 36/72 ( divide AMBOS por 36)

x'' = 1/2

E) (x+1)²=x+7

(x + 1)(x + 1) = x + 7

x² + 1x + 1x + 1 = x + 7

x² + 2x + 1 = x + 7

x² + 2x + 1 - x - 7 = 0

x² + 2x - x + 1 - 7 = 0

x² + 1x - 6 = 0

a = 1

b = 1

c = - 6

Δ = b² - 4ac

Δ = (1)² - 4(1)(-6)

Δ = + 1 + 24

Δ = + 25 ---------------------------> √Δ = 5 (√25 = 5)

se

Δ > 0 ( DUAS raizes diferentes)

(baskara)

(-b + - √Δ)

x = -----------------

2a

x' = - 1 - √25/2(1)

x' = - 1 - 5/2

x' = - 6/2

x' = - 3

e

x'' = - 1 + √25/2(1)

x'' = - 1 + 5/2

x'' = + 4/2

x'' = 2