Question

ROZWIĄŻ RÓWNANIA:

1.4x2-3x=0

2.3x2+2x=0

3.7x-x2=0

4.2x2=x

5.8x=4x2

6.4x2-9=0

7.16x2-25=0

8.4-100x2=0

9.9x2=1

10.4x2-121=0

11.x2+6x+9=0

12.x2-10x+25=0

13.x2-4x+7=0

14.x2-4x+1=0

15.2x2-9x-35=0

PROSZE ZRÓBCIE MI BO JA TEGO WOGLE NIE UMIEM

Answer 1

1.

4x²-3x=0

x(4x-3) = 0

4x-3 =0  lub x=0

4x-3=0

4x= 3

x= 3/4

 

2.

3x²+2x=0

x(3x+2) =0

3x+2=0   lub  x=0

3x=-2

x= -2/3

 

3.

7x-x²=0

x(7-x) = 0

7-x = 0 lub x=0

x= 7

 

4.

2x²=x

2x² -x = 0

x(2x -1)=

2x-1 = 0 lub  x=0

2x=1

x= 1/2

 

5.

8x=4x²

8x-4x² =0

4x(2-x)=0

2-x=0   lub 4x=0

x=2   lub x=o

 

6.

4x²-9=0

(2x-3) (2x+3)=0

2x-3 = 0  lub  2x+3 =0

2x=3                      2x=-3

x= 3/2 =1 ½      lub   x=-3/2 = - 1 ½

 

7.

16x²-25=0

(4x-5)(4x+5) =0

4x-5 =0  lub  4x+5 =0

4x=5              4x=-5

x= 5/4 = 1 ¼    lub    x=-5/5 = -1 ¼

 

8.

4-100x²=0

(2-10x)(2+10x)=0

2-10x = 0  lub  2+10x= 0

10x=2       lub   10x =-2

x= 2/10=1/5    lub x=  -1/5

 

9.

9x²=1

9x² -1 = 0

(3x-1)(3x+1)=0

3x-1 =0    lub  3x+1 = 0

3x= 1               3x = -1

x= ½      lub      x= - ½  

 

10.

4x²-121=0

(2x-11) (2x+11) = 0

2x-11 =0   lub   2x+11 = 0

2x =11                2x= -11     

x= 11/2 = 5 ½   lub   x=-11/2 = - 5 ½

 

11.

x²+6x+9=0

Δ= b² - 4ac = 6² - 4*1*9 = 36 -36 =0

x₀ = -b/2a =-6/2 =-3

 

12.

x²-10x+25=0

Δ= b² - 4ac = (-10)² - 4*1*25 = 100 -100 =0

x₀ = -b/2a =10/2 = 5

 

13.

x²-4x+7=0

Δ= b² - 4ac = (-4)² - 4*1*7 =16 – 28 = 0

nie ma rozwiązań

 

14.

x²-4x+1=0

Δ= b² - 4ac = (-4)² - 4*1*1 = 14 -4 = 12

√Δ = √12 =√4*3 = 2√2 = 2*1,73 ≈3,46

x₁ = (-b-√Δ)/2a = (4-3,46)/2 = 0,54/2 =0,27 ≈0,3

x₂ = (-b+√Δ)/2a = (4+3,46)/2 = 7,46/2 =3,73 ≈3,7

 

15.

2x²-9x-35=0

Δ= b² - 4ac = (-9)² - 4*2*(-35) =81 +280=361

√Δ = √361 =19

x₁ = (-b-√Δ)/2a = (9-19/4 = -10/4 = -2 ½

x₂ = (-b+√Δ)/2a = (9+19/4 = 28/4 = 7