Question

Rozwiąż równania:

3.39 do D

Rozwiąż nierówości:

3.40 do D

Answer 1

3.39.

a) (x-3)(x+2) + (5 - x)(x + 1) = 0

x^2 + 2x - 3x - 6 + 5x + 5 - x^2 - x = 0

-2x - 6 + 5x + 5 = 0

3x = 1

x = 1/3

 

b) (2x +1)(x -4) = 2(1 - x)(5 - x)

2x^2 - 8x + x - 4 = 2(5 - x - 5x + x^2)

2x^2 - 7x - 4 = 10 - 12x + 2x^2

19x = 14

x = 14/19

 

c) 4x - (x + 5)(x - 7) = x(1 - x)

4x - (x^2 - 7x + 5x - 35) = x - x^2

4x + 7x - 5x + 35 = x

6x - x = -35

5x = - 35

x = -7

 

d) (x - 2)(4 + x) = (x + 3)(x - 1)

4x + x^2 - 8 - 2x = x^2 - x + 3x -3

2x - 8 = 2x -3

2x - 8 = 2x -3

0 = -5

równanie sprzeczne

 

3.40.

a) 5x(x-7) - 2(x^2 + 1) =< (1 - 3x)(6 - x)

5x^2 - 35x - 2x^2 - 2 =< 6 - x - 18x + 3x^2

-35x - 2 =< 6 - x - 18x

-34x =< 8 - 18x

-16x =< 8

x <= - 0,5

 

b) 1 - (1 - x)(-x - 1) - 2x > 6 - x^2

1 - (-x - 1 + x^2 +x) - 2x > 6 - x^2

1 + x +1 - x^2 - x - 2x > 6 - x^2

2 - 2x > 6

-4 > 2x

x < -2

 

c) -2(7x -4)(x - 7) =< 1 + 7(7 - 2x^2)

-2(7x^2 - 49x - 4x + 28) =< 1 + 49 - 14x^2

-14x^2 + 98x + 8x - 56 =< 50 - 14x^2

106x - 56 =< 50

106x =< 106

x =< 1

 

d) -4(x + 2)(1 + x) > 2(1 - 2x^2)

-4(1 + x^2 + 2 + 2x) > 2 - 4x^2

-4 - 4x^2 - 8 - 8x > 2 - 4x^2

-12 - 8x > 2

 -14 > 8x

x < 1,75