Odpowiedzi

2009-12-16T23:16:44+01:00
Zad 7.
a) D=R-{-1,2}

2x-3 x 2x - 3 - x - 1 x x - 4 x
------ - 1 = ----- = ---------------- = ------ = ------ = ---- =
x + 1 x-2 x + 1 x-2 x+1 x-2

(x-4)(x-2) = x(x+1) = x^2 -2x -4x +8 = x^2 + x =

-7x = -8

x = 8/7

---------------------------------------------------------------------

b) D=R-{-3,2}

x^2 -4 (x-2)(x+2)
------------ = ------------- =
(x-2)(x+3) (x-2)(x+3)

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

x=2 lub x=-2
---------------------------------------------------------------------

zad 8.
a)
D=R-{-1/4}
3-x
------ ≥ 0
4x+1

(3-x)(4x+1)≥0

x=3 lub x=-1/4

x e <-1/4, 3>
---------------------------------------------------------------------
b) D=R-{-3,-2,-1}

1 2 3
------- + ------ > ------
x+1 x+3 x+2

x+3 + 2x + 2 3
--------------- > ------
(x+1)(x+3) x+2

3x + 5 3
------------- - ----- > 0
(x+1)(X+3) X+2

(3x+5)(x+2) - 3(x+1)(x+3)
------------------------------ > 0
(x+1)(x+3)(x+2)

3x^2 +6x +5x + 10 - 3(x^2 +3x + x +3)
---------------------------------------------- > 0
(x+1)(x+3)(x+2)

3x^2 +11x + 10 - 3x^2 - 12x -9
----------------------------------------- >0
(x+1)(x+3)(x+2)

1-x
---------------------- <0
(x+1)(x+3)(x+2)

(1-x)(x+1)(x+3)(x+2) <0

x = 1 lub x =-1 lub x=-3 lub x = -2

x e (-∞ , -3) lub (-2,-1) lub (1, +∞)
----------------------------------------------------------------------

zad 10.

x^3 - 2x^2 -3x
W(x) = ------------------------
x^6 - 18x^4 +81x^2

a)
x^6 - 18x^4 +81x^2 = 0
x^2( x^4 - 18x^2 +81) =0

x^4 - 18x^2 +81

x^2 = t≥0

t^t -18t +81 = 0

Delta = 324 - 324 = 0

t = 9

x^2 = 9
x= 3 lub x = -3

D -R - {-3,0,3}
-----------------------------------------------------------------
b)

x^3 - 2x^2 -3x
W(x) = ------------------------
x^6 - 18x^4 +81x^2


x^3 - 2x^2 -3x
W(x) = ------------------------
x^2(x+3(x-3)

= x(x^2 - 2x -3)

delta = 4 +12 = 16

pierwiastek z delty = 4

x1 = -1 x2= 3

x(x+1)(x-3)
W(x) = ------------------------
x^2(x+3)(x-3)
--------------------------------------------------------------------

zad 11.

x-2 x^2 -1 1
------ + --------------- - ----
x^2-4x x^2 - 8x +16 2x


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

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

---------------------------------------------------------------------



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zad 15.

A(4,2)
S(2,1)

(4-2)^2 + (2-1)^2 = r^2