Question

rozwiaz nierownosc kwadratową :

x(x+6)>-9

3x+7>bądź równe 4x^2

Answer 1

1)

 

x(x+6)>-9

+6x+9>0

delta= 6^{2} - 4*1*9

delta=0

x0= -6/2=-3

x należy);-3)(-3;\infty)

Answer 2

1) x(x+6) > -9

x² + 6x > -9

x² + 6x + 9 > 0

 

a=1 , b=6 , c=9

 

Δ = b² - 4ac

Δ = 6² - 4 * 1 * 9

Δ = 36 - 36

Δ = 0

 

x₀ = -b | 2a

x₀ = -6 | 2*1

x₀ = -6 | 2

x₀ = -3

 

x ∈ ( -∞ , -3 ) u ( -3 , +∞ )

 

2) 3x + 7 ≥ 4x²

-4x² + 3x + 7 ≥ 0

 

a=-4 , b=3 , c=7

 

Δ = b² - 4ac

Δ = 3² - 4 * (-4) * 7

Δ = 9 + 112

Δ = 121

 

x₁ = -b - √Δ | 2a

x₁ = -3 - √121 | 2*(-4)

x₁ = -3 - 11 | -8

x₁ = -14 | -8

x₁ = 1¾ = 1,75

 

x₂ = -b +√Δ | 2a

x₂ = -3 + √121 | 2*(-4)

x₂ = -3 + 11 | -8

x₂ = 8 | -8

x₂ = -1

 

x ∈ < -1 ; 1,75 >