Question

Resolva as equações a seguir

a) x2 - 26x + 169 = 0

b) x2 - 2x - 3= 0

c) x2 - 16x + 64 = 0

Answer 1

a) x² - 26x + 169 = 0

a = 1

b = -26

c = 169

Δ = b² - 4 .a .c

Δ = (-26)² - 4 .1 .169

Δ = 676 - 676

Δ = 0

x = -b ± $\sqrt{Delta}$ /2 .a

x = -(-26) ± $\sqrt{0}$ /2 .1

x = 26 ± 0 /2

x = 26 /2 = 13

  S = (13)

b) x² - 2x - 3 = 0

a = 1

b = -2

c = -3

Δ = b² - 4 .a .c

Δ = (-2)² - 4 .1 .(-3)

Δ = 4 + 12

Δ = 16

x = -b ± $\sqrt{Delta}$ /2 .a

x = -(-2) ± $\sqrt{16}$ /2 .1

x = 2 ± 4 /2

x' = 2 + 4 /2

x' = 6 /2 = 3

x" = 2 - 4 /2

x" = -2 /2 = -1

  S = (3, -1)

c) x² - 16x + 64 = 0

a = 1

b = -16

c = 64

Δ = b² - 4 .a .c

Δ = (-16)² - 4 .1 .64

Δ = 256 - 256

Δ = 0

x = -b ± $\sqrt{Delta}$ /2 .a

x = -(-16) ± $\sqrt{0}$ /2 .1

x = 16 ± 0 /2

x = 16 /2 = 8

  S = (8)