Question

Rozwiąż równania

(x+5)^2 > lub równe ( 2x+10) ^2

-4x^2 < 1

(2x+5)^2 - (2x-5)^2 = 3x^2 + 41x - 4

Answer 1

(x + 5)² ≥ (2x + 10)²
x² + 10x + 25 ≥ 4x² + 40x + 100
- 4x² + x² + 10x - 40x + 25 - 100 ≥ 0
- 3x² - 30x - 75 ≥ 0 / : - 3
x² + 10x + 25 ≤ 0
a = 1
b = 10
c = 25
Δ = b² - 4ac = 10² - 4 * 1 * 25 = 100 - 100 = 0
xo = - b/2a = - 10/2 = - 5
x = {- b/2a) = - 5

- 4x² < 1
- 4x² - 1 < 0
4x² + 1 > 0
x ∈ R
(2x + 5)² - (2x - 5)² = 3x² + 41x - 4
4x² + 20x + 25 - 4x² + 20x - 25 = 3x² + 41x - 4
40x = 3x² + 41x - 4
3x² + 41x - 40x - 4 = 0
3x² + x - 4 = 0
a = 3
b = 1
c = - 4
Δ = b² - 4ac = 1 - 4 * 3 * - 4 = 1 + 48 = 49
√Δ = √49 = 7
x₁ = (- b - √Δ)/2a = ( - 1 - 7)/6 = - 8/6 = - 4/3
x₂ = ( - b + √Δ)/2a = ( - 1 + 7)/6 = 6/6 = 1
3(x + 4/3)(x - 1) = 0
x + 4/3 = 0 lub x - 1 = 0
x = - 4/3 lub x = 1