Question

1 zadanie Rozwiąż równania i nierówności a)x ²-9=3(x-2)(+3) b) x-1<4x ² 2 zadanie Oblicz 2 cos30°+tg60°)²-(4sim45°+ctg45°)²

Answer 1

a)x ²-9=3(x-2)(x + 3)

x² - 9 = 3(x² + 3x - 2x - 6)

x² - 9 = 3x² + 3x - 18

x² - 3x² - 3x - 9 + 18 = 0

-2x² - 3x + 9 = 0

2x² + 3x - 9 = 0

Δ = 9 + 2 * 2 * 9 = 9 + 36 = 45

√Δ = 3√5

x1 = (-3 - 3√5) / 4

x2 = ( - 3 + 3√5)/4 

 

b) x-1<4x²

4x² - x + 1 > 0

Δ = 1 - 4 * 4 * 1 = 1 - 16 = -15 < 0

a = 4 > 0

x ∈ R 

 

2.

 (2cos30°+tg60°)²-(4sim45°+ctg45°)² = (2 * √3/2  + √3)² - (4 * √2/2 + 1)² =

(2√3)² - (2√2 + 1)² = 12 - 8 - 4√2 - 1 = 3 - 4√2