Question

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Answer 1

Odpowiedź:

zad 1

a)

9x² - 49 = 0

(3x - 7)(3x + 7) = 0

3x - 7 =0 ∨ 3x + 7 = 0

3x = 7 ∨ 3x = - 7

x = 7/3 ∨ x = - 7/3

x = 2 1/3 ∨ x = - 2 1/3

b)

x² + 8x + 16 = 0

a =1 , b = 8 , c = 16

Δ = b² - 4ac = 8² - 4 * 1 * 16 = 64 - 64 = 0

x₁ = x₂ = - b/2a = - 8/2 = - 4

c)

x² - (2 - x)(2 + x) = x² - (4 - x²) = x² - 4 + x² = 2x² - 4

2x² - 4 = 0

(√2x - 2)(√2x + 2) = 0

√2x - 2 = 0 ∨ √2x + 2 = 0

√2x = 2 ∨ √2x = - 2

x = 2/√2 ∨ x = - 2/√2

x = 2√2/2 ∨ x = - 2√2/2

x = √2 ∨ x = - √2

d)

2x² - 9x - 35 = 0

a = 2 , b = - 9 , c = - 35

Δ = b² - 4ac = (- 9)² - 4 * 2 * (- 35) = 81 + 280 = 361

√Δ = √361 = 19

x₁ = (- b - √Δ)/2a = (9 - 19)/4 = - 10/4 = - 2 2/4 = - 2 1/2 = - 2,5

x₂ = (- b + √Δ)/2a = (9 + 19)/4 = 28/4 = 7

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