Question

Assistindo os vídeos com seus links acima, resolva as atividades a seguir:

Answer 1

Todas as equações são de segundo grau, logo temos que achar x' e x" :

a) 9$x^{2}$ - 3x = 0

Δ = -3² - 4 . 9 . 0

Δ = 9 - 0

Δ = 9

x = 3 ± √9 / 2.-3

x' = 3 + 3 / -6

x' = -1

x" = 3 - 3 / 2.-3

x" = 0

b) 10$x^{2}$ + 5x = 0

Δ = 5² - 4 . 10 . 0

Δ = 25 - 0

Δ = 25

x = - 5 ± √25 / 2.10

x' = -5 + 5 / 20

x' = 0

x" = -10 / 20

x" = -1/2

c) 2$x^{2}$ - 4x = 0

Δ = -4² - 4 . 2 . 0

Δ = 16 - 0

Δ = 16

x = 4 ± √16 / 2.-4

x' = 4 + 4 / -8

x' = - 1

x" = 4 - 4 / -8

x" = 0

d) 12$x^{2}$ - 8x = 0

Δ = -8² - 4 . 12 . 0

Δ = 64 - 0

Δ = 64

x = 8 ± √64 / 24

x' = 8 + 8 / 24

x' = 2/3

x" = 8 - 8 / 24

x" = 0

e) 10$x^{2}$ - 70x = 0

Δ = -70² - 4 . 10 . 0

Δ = 4900 - 0

Δ = 4900

x = 70 ± √70 / 2.10

x' = 70 + 70 / 20

x' = 7

x" = 70 - 70 / 20

x" = 0

f) 7$x^{2}$ = - 21x  ⇒  7$x^{2}$  + 21x = 0

Δ = 21² - 4 . 7 . 0

Δ = 441 - 0

Δ = 441

x = 21 ± √441 / 2.7

x' = 21 + 21 / 14

x' = 3

x" = 21 - 21 / 14

x" = 0

g) $x^{2}$ - 169 = 0

Δ = 0² - 4 . 1 . -169

Δ = 0 + 676

Δ = 676

x = 0 ± √676 / 2.1

x' = 0 + 26 / 2

x' = 13

x" = 0 - 26 / 2

x" = -13

h) 2$x^{2}$ - 98 = 0

Δ = 0² - 4 . 2 . -98

Δ = 0 + 784  

Δ = 784

x = 0 ± √784 / 2.2

x' = 0 + 28 / 4

x' = 7

x" 0 - 28 / 4

x" = - 7

i) $x^{2}$ - 36 = 0

Δ = 0² - 4 . 1 . -36

Δ = 0 + 144

Δ = 144

x = 0 ± √114 / 2.1

x' = 0 + 12 / 2

x' = 6

x" = 0 - 12 / 2

x" -6

j) 5$x^{2}$ = 125  ⇒  5$x^{2}$  - 125 = 0

Δ = 0² - 4 . 5 . -125

Δ = 0 + 2500  

Δ = 2500

x = 0 ± √2500 / 2.5

x' = 0 + 50 / 10

x' = 5

x" = 0 - 50 / 10

x" -5

k) 2$x^{2}$ - 128 = 0

Δ = 0² - 4 . 2 . -128

Δ = 0 + 1024

Δ = 1024

x = 0 ± √1024 / 2.2

x' = 0 + 32 / 2.2

x' = 8

x" = 0 - 32 / 2.2

x" = -8

Espero ter ajudado ;)