Question

3xkwadrat-2(pierwiastek3x)+1

2)6xkwadrat -12

3)27+y do potegi 3

4)x3-9x2+27x-27

(x2+2x+4)(x-2)2

6)(x-1)(x2+x+1)(x3+1)

7)(9x4-3x2+1)(3x2+1)

równania i nierówności

1)8-x2>0

2)-1/25*x2>0

3)x2=4x

4)3+x2<0

5)49=-4x2

Answer 1

Δ = b²-4*a*c

x₁ = (-b-√Δ)/2a

x₂ = (-b+√Δ)/2a

 

1)

3x²-2(√3x)+1

3x²-2√3x+1

a=3 b =2√3 c=1

Δ = (2√3)²-4*3*1 = 12-12 = 0

x = (-2√3)/ 6 = -⅓√3

 

2)

6x² -12

6x² =12 |:6

x² = 2

x = √2

 

3)

27+y³

y³ = -27

y = -3

 

4)

x³-9x²+27x-27

x²(x-9)+27(x-1)

(x²+27)(x-9)(x-2) = 0

x² = -27 x∉

x = 9

x = 2

 

5)

(x²+2x+4)(x-2)² = (x²+2x+4)(x²-4x+4)

Δ = 4-4*1*4 = -8

Δ = 16-4*1*4 = 0

x = 4/2 = 2

 

6)

(x-1)(x²+x+1)(x³+1)

x = 1

Δ = 1-4*1*1 = 1-4 = - 3

x = -1

 

7)

(9x⁴-3x²+1)(3x²+1)

x² = t

9t²-3t+1 = 0

Δ = 9-4*9*1 = 9-36 = -27

3x² = -1 |:3

x²=-1/3

x∉

 

 

równania i nierówności

1)8-x²>0

x² < 8

x < √8

 

2)

-1/25*x²>0

x² > 1/25

x > ±1/5

 

3)

x²=4x

x²-4x = 0

x(x-4)

x = 0

x = 4

 

4)

3+x²<0

x²<-3

x∉

 

5)

49=-4x² |:(-4)

x² = -12,25

x ∉

Answer 2

W załączniku.