Question

Rozwiąż równania:

a. I2x-1I = 7
b. 2x-x^2=0
c. (5x+3)^2 = 2

d. (4x+3)^2 = 3
e. x- 3x^2 = 0

Answer 1

a)  I2x-1I = 7

2x-1 >= 0,  I2x-1I = 2x-1

2x-1 =7

2x = 8

x = 4

=====

2x-1 < 0,  (2x-1) =1-2x

1-2x = 7

-2x = 6

x = -3

======

x = 4,  v  x = -3

 

b)

2x-x^2 = 0

x(2-x) = 0

x = 0

===== lub

2-x = 0

x = 2

=====

x = 0 ,  v  x = 2

 

c)

(5x+3)^2 = 2

25x^2 +30x+9 = 2

25x^2 +30x +7 = 0

D = 900 -(4*25*7) = 900- 700 = 200

VD =10V2

x1 =(-30 -10V2)/50 =(-3-V2)/5

x2 =(-30+10V2)/50 =(-3+V2)/5

 

x =(-3V2)/5,   v   x =(-3+V2)/5

 

d)

(4x+3)^2 =3

16x^2 +24x+9 =3

16x^2 +24x+6 = 0 I:2

8x^2 +12x+3 = 0

D =144 -(4*8*3) =144-96 = 48

VD = 4V3

x1 =(-12-4V3)/16 =(-3-V3)/4

x2 =(-12+4V3)/16 =(-3+V3)/4

 

x =(-3-V3)/4,   v   x =(-3+V3)/4

 

e)

x-3x^2 = 0

x(1-3x) = 0

x = 0

===== lub

1-3x = 0

3x =1

x = 1/3

=======

x = 0,  v  x =1/3