Question

Помогите пожалуйста быстро.

Answer 1

1) 9x = - 2x² - 10

2x² + 9x + 10 = 0

D = 9² - 4 * 2 * 10 = 81 - 80 = 1

x₁₂ = - 9 ± √1 / 2 * 2

x₁ = - 9 + 1 / 2 * 2 = -8 / 4 = - 2

x₂ = -9 - 1 / 2 * 2 = -10 / 4 = - 5 / 2 = - 2,5

Ответ: x₁ = - 2,5 ; x₂ = - 2

2) x² - 6x = 0

x ( x - 6 ) = 0

x - 6 = 0 ; x =0

x = 6

Ответ: x₁ = 0, x₂ = 6

3) 11 + x² + 6x = 0

x² + 6x + 11 = 0

D = 6² - 4 * 11 = 36 - 44 =  -22

D < 0 ⇒ x∉

Ответ: Нет решения

4) 3 + x² = 4x

x² - 4x + 3 = 0

D = (-4)² - 4 * 3 = 16 - 12 = 4

x₁₂ = 4 ± √4 / 2 * 1

x₁ = 4 + 2 / 2 * 1 = 6 / 2 = 3

x₂ = 4 - 2 / 2 * 1 = 2 / 2 = 1

Ответ: x₁ = 1 , x₂ = 3

5) x² - 1,21 = 0

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

x - 1,1 = 0 ; x + 1,1 = 0

x = 1,1 ; x = - 1,1

Ответ: x₁ = - 1,1 , x₂ = 1,1

6) 9x² + 4 + 12x = 0

9x² + 12x + 4 = 0

(3x + 2)² = 0

3x + 2 = 0

3x = -2

x = -2/3

Или

D = 12² - 4 * 9 * 4 = 144 - 144  = 0

x = - 12  / 9 * 2 = - 12/ 18 = - 2/3

Ответ: x = - 2/3

7) 7t² - 4t - 3 = 0

D = (-4)² - 4 * 7 * ( - 3) = 16 + 84 = 100

t₁₂ = 4 ± √100 / 2 * 7

t₁ = 4 + 10 / 2 * 7 = 14 / 14 = 1

t₂ = 4 - 10 / 2 * 7 = - 6 / 14 = - 3/7

Ответ: t₁ = - 3/7 , t₂ = 1