Question

5) Resolva as seguintes equações do 2° grau:

a) x² - 49 = 0

b) x² = 1

c) 2x² - 50 = 0

d) 7x² - 7 = 0

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Answer 1

Resposta:

a) x' = 7 || x'' = -7

b) x' = 1 || x'' = -1

c) x' = 5 || x'' = -5

d) x' = 1 || x'' = -1

Explicação passo a passo:

a)

x² - 49 = 0

Δ = 0² - 4.1.(-49)

Δ = 0 + 196

Δ = 196

- 0 ± √196 / 2.1

0 ± 14 / 2

x' = 0 + 14 / 2 → 14 / 2 = 7

x'' = 0 - 14 / 2 → -14 / 2 = -7

b)

x² = 1

x² - 1 = 0

Δ = 0² - 4.1.(-1)

Δ = 0 + 4

Δ = 4

- 0 ± √4 / 2.1

0 ± 2 / 2

x' = 0 + 2 / 2 → 2 / 2 = 1

x'' = 0 - 2 / 2 → -2 / 2 = -1

c)

2x² - 50 = 0

Δ = 0² - 4.2.(-50)

Δ = 0 + 400

Δ = 400

- 0 ± √400 / 2.2

0 ± 20 / 4

x' = 0 + 20 / 4 → 20 / 4 = 5

x'' = 0 - 20 / 4 → -20 / 4 = -5

d)

7x² - 7 = 0

Δ = 0² - 4.7.(-7)

Δ = 0 + 196

Δ = 196

- 0 ± √196 / 2.7

0 ± 14 / 14

x' = 0 + 14 / 14 → 14 / 14 = 1

x'' = 0 - 14 / 14 → -14 / 14 = -1

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