Question

ME AJUDEM

Resolva as equações
a) x²-4x+3=0
b)x² + 6x +5 =0
c)x² - 12x +27=0
d)x² + 8x + 15=0
e)x² - 10x + 19=0

Ex: x² +10x +24=0
x²+ 10x +24 +1 =0+1
x² +10x +25 =1
(x + 5)² = 1
x +5 =1
x=-4 ou x + 5 = -1
x=-6

Answer 1

a)
x² - 4 x + 3 = 0
a = 1; b = - 4; c = 3

Δ = b² - 4ac
Δ = 16 - 4.1.3
Δ = 16 - 12
Δ = 4

x = - b +/- √Δ
          2a

x = 4 + 2 = 6 = 3
         2       2

x = 4 - 2 = 2 = 1
         2      2

x = 1 e x = 3
*************************
(ou)

x² - 4x + 3 + 1 = 0 + 1
x² - 4x + 4 = 1
(x - 2)² = 1
x - 2 = √1
x - 2 = +/-1

x - 2 = 1
x = 1 + 2
x = 3

x - 2 = - 1
x = - 1 + 2
x = 1

b)
x² + 6x +5 =0
a = 1; b = 6; c = 5

Δ = b² - 4ac
Δ = 36 - 4.1.5
Δ = 36 - 20
Δ = 16

x = - b +/- √Δ = - 6 +/- √16
          2a                2.1

x = - 6 + 4 = - 2/2 = - 1
          2
x = - 6 - 4 = - 10/2 = - 5
          2

x = - 1 e x = - 5
*********************************************

c)
x² - 12x +27 = 0
a = 1; b = - 12; c = 27

Δ = b² - 4ac
Δ = 144 - 4.1.27
Δ = 144 - 108
Δ = 36

x = - b +/- √Δ = - ( - 12) +/-√36 
            2a               2.1

x = 12 + 6 = 18/2 = 9
         2

x = 12 - 6 = 6/2 = 3
         2

x = 9 e x = 3
*****************************************************
d)
x² + 8x + 15 = 0
a = 1; b = 8; c = 15

Δ = b² - 4ac
Δ = 64 - 4.1.15
Δ = 64 - 60
Δ = 4

x = - b +/- √Δ = - 8 +/- √4   
           2a              2.1

x = - 8 + 2 = - 6/2 = - 3
           2

x = - 8 - 2 = - 10/2 = - 5
          2

x = - 3 e x = - 5
**********************************

e)
x² - 10x + 19 = 0
a = 1; b = - 10; c = 19

Δ = b² - 4ac
Δ = 100 - 4.1.19
Δ = 100 - 76
Δ = 24 
√Δ = √24 = √4.√6 = 2√6

x = - b +/- √Δ = - ( - 10) +/- √24 
          2a                   2.1

x' = 10 + 2√6 = 5 + √6
          2

x" = 10 - 2√6 = 5 - √6
          2