Question

Rozwiąż równanie......

Answer 1

∆=3²-4*1*(-18)=9+72=81

√∆=9

x∈{-6;3}

x∈{-1;1}

x∈{-√2;√2}

∆=1-4*1*1=1-4=-3

Brak rozwiązania, bo delta mniejsza od zera

Answer 2

Odpowiedź:

zad 11

a)

(x² + 3x)/2 - (x² + 7)/3 = (3x + 2)/3  | * 6

3(x² + 3x) - 2(x² + 7) = 2(3x + 2)

3x² + 9x - 2x² - 14 = 6x + 4

x² + 9x - 14 = 6x + 4

x² + 9x - 6x - 14 - 4 = 0

x² + 3x - 18 = 0

a = 1 , b = 3 , c = - 18

Δ = b² - 4ac = 3² - 4 * 1 * (- 18) = 9 + 72 = 81

√Δ  = √81 = 9

x₁ = ( - b - √Δ)/2a = (- 3  - 9)/2 = - 12/2 = - 6

x₂ = (- b + √Δ)/2a = (- 3 + 9)/2 = 6/2 = 3

b)

(x² - 3)/8 - x²/4 = (x² + 6)/2 + x² - 5  | * 8

x² - 3 - 2x² = 4(x² + 6) + 8x² - 40

- x² - 3 = 4x² + 24 + 8x² - 40

- x² - 3 = 12x² - 16

- x² - 12x² = - 16 + 3

- 13x² = - 13 | : (- 13)

x² = 1

x² - 1 = 0

(x - 1)(x + 1) = 0

x - 1 = 0 ∨ x + 1 = 0

x = 1 ∨ x = - 1

c)

x(x + 7) - 5(x - 7)(x - 6) = 6(2x + 3)² - 320

x² + 7x - 5(x² - 7x - 6x + 42) = 6(4x² + 12x + 9) - 320

x² + 7x - 5(x² - 13x + 42) = 24x² + 72x + 54 - 320

x² + 7x  - 5x² + 65x - 210 = 24x² + 72x - 266

- 4x² + 72x - 210 = 24x² + 72x - 266

- 4x² - 24x² + 72x - 72x = - 266 + 210

- 28x² = - 56 | : (- 28)

x² = 2

x² - 2 = 0

(x - √2)(x + √2) = 0

x - √2  = 0 ∨ x + √2  = 0

x = √2 ∨ x = - √2

d)

x[(x - 1)(x + 1) + x(1 - x)] = x[(x - 1)(x + 1) - x²]

x(x² + x - x²) = x(x² - 1 - x²)

x * x = x * (- 1)

x² = - x

x² + x = 0

x(x + 1) = 0

x = 0 ∨ x + 1  = 0

x = 0 ∨ x = - 1