Question

1)Resolva em IR

A)
$9 {y}{2} - 3y - 2 = 0$
B)
$2 {n}^{2} + 7n + 6 = 0$
C)
$3 {x}^{2} + 8x - 3 = 0$
D)
$3 {x}^{2} - 7x + 4 = 0$

Answer 1

Boa tarde

a) 

9y² - 3y - 2 = 0

delta
d² = 9 + 72 = 81
d = 9

y1 = (3 + 9)/18 = 12/18 = 2/3
y2 = (3 - 9)/18 = -6/18 = -1/3 

b)

2n² + 7n + 6 = 0

delta
d² = 49 - 48 = 1
d = 1

n1 = (-7 + 1)/4 = -3/2
n2 = (-7 - 1)/4 = -2 

c)

3x² + 8x - 3 = 0

delta
d² = 64 + 36 = 100
d = 10

x1 = (-8 + 10)/6 = 1/3
x1 = (-8 - 10)/6 = -3 

d)

3x² - 7x + 4 = 0

delta
d² = 49 - 48 = 1
d = 1

x1 = (7 + 1)/6 = 4/3
x2 = (7 - 1)/6 = 1

Answer 2

Olá!!!

Resolução!!!

9y² - 3y - 2 = 0

a = 9, b = - 3, c = - 2

∆ = b² - 4ac
∆ = ( - 3 )² - 4 • 9 • ( - 2 )
∆ = 9 + 72
∆ = 81

y = - b ± √∆ / 2a
y = - ( - 3 ) ± √81 / 2 • 9
y = 3 ± 9 / 18
y' = 3 + 9 / 18 = 12/18 : 6 : 2/3
y" = 3 - 9 / 18 = - 6/18 : 6 : - 1/3

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

b)

2n² + 7n + 6 = 0

a = 2, b = 7, c = 6

∆ = b² - 4ac
∆ = 7² - 4 • 2 • 6
∆ = 49 - 48
∆ = 1

n = - b ± √∆ / 2a
n = - 7 ± √1 / 2 • 2
n = - 7 ± 1 / 4
n' = - 7 + 1 / 4 = - 6/4 : 2 = - 3/2
n" = - 7 - 1 / 4 = - 8/4 = - 2

S = { - 3/2, - 2 }

c)

3x² + 8x - 3 = 0

a = 3, b = 8, c = - 3

∆ = b² - 4ac
∆ = 8² - 4 • 3 • ( - 3 )
∆ = 64 + 36
∆ = 100

x = - b ± √∆ / 2a
x = - 8 ± √100 / 2 • 3
x = - 8 ± 10 / 6
x' = - 8 + 10 / 6 = 2/6 : 2 = 1/3
x" = - 8 - 10 / 6 = - 18/6 = - 3

S = { - 3, 1/3 }

d)

3x² - 7x + 4 = 0

a = 3, b = - 7, c = 4

∆ = b² - 4ac
∆ = ( - 7 )² - 4 • 3 • 4
∆ = 49 - 48
∆ = 1

x = - b ± √∆ / 2a
x = - ( - 7 ) ± √1 / 2 • 3
x = 7 ± 1 / 6
x' = 7 + 1 / 6 = 8/6 : 2 = 4/3
x" = 7 - 1 / 6 = 6/6 = 1

S = { 1, 4/3 }

Espero ter ajudado!!!