Question

Ajudem Pfv
Resolva as inequações produto e quociente:

a) (-x + 1 ) . (5 x 2) > 0


b) - x . (2x - 1 ) . ( x - 3 ) < 0


c) ( 1 - 2x ) . ( 3 + 4x )
____________________ > 0
4 - X


d) X
_______ < 1
X - 1 ​

Answer 1

Resposta:

a) (-x + 1 ) . (5 x 2) > 0

(5 x 2) ..não sei se é 5x²   , ou 5x+2   ou 5x-2 ...

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

b)

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

p=-x   ..raiz x=0   ==>a=-1 <0

p+++++++++++++(0)---------------------------

q=2x-1  ...raiz x=1/2  ...a=2>0

q-------------------(1/2)+++++++++++++++++

t=x-3 ..........raiz  x=3  ..a=1>0

t---------------------(3)++++++++++++++++++++

Estudo de sinais:

p+++++++++(0)--------------------------------------------

q-------------------------(1/2)+++++++++++++++++

t----------------------------------------(3)++++++++++++++++++++

p*q*t++++++(0)------(1/2)++++(3)------------------------------

0 < x < 1/2  U x >3

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

c)

(1-2x)*(3+4x)/(4-x)  >0

q=1-2x   ...raiz x=1/2  ...a=-2<0

q++++++++++++++(1/2)----------------------

p=3+4x ...raiz x= -3/4  ..a=4>0

p-----------------------(-3/4)+++++++++++++++

t=4-x ...raiz x =4  ...a=-1<0

t++++++++++++++(4)-----------------------------

Estudo de sinais:

q++++++++++++++++(1/2)--------------------------------------

p----------(-3/4)++++++++++++++++++++++++++++++++++

t++++++++++++++++++++++++++++(4))---------------------

q-----------(-3/4)+++++(1/2)-------------(4)+++++++++++++++

(-3/4)<x<1/2  U x>4

d)

x/(x-1) -1 < 0

(x-x+1)/(x-1) < 0

1/(x-1) <0

p=x-1  ..raiz x=1   a=1>0

p-------------------(1)+++++++++++++

x < 1

Answer 2

Resposta:

a) (-x+1)(5 · 2) > 0

(-x+1)(10)>0

-10x+10 > 0

-10x > -10

x > 1

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

(-2x²+x)(x-3) < 0

-2x³+6x²+x² - 3x < 0

-2x³ + 7x² - 3x < 0

x(-2x²+7x-3) < 0

x < -(-2)+-√(7)²-4(-2)(-3)/2(-2)

x < 2 +- √49 - 24 / -4

x < 2 +- √25/-4

x < 2 +- 5 / - 4

x < 2 + 5 / -4 = -7/4

x < 2 - 5 / -4 = -3/-4 = 3/4

c ) (1-2x)(3+4x)/4-x > 0

3 + 4x -6x - 8x² / 4 - x > 0

-8x² - 2x + 3 / 4 - x > 0

4 - x ≠ 0

-x ≠ - 4 (-1)

x ≠ 4

x > -(-2)+-√(-2)²-4(-8)(3)/2(-8)

x > 2 +- √4 + 96/ -16

x > 2 +-√100 / -16

x > 2 +- 10/-16

x' > 12/-16 = -3/4

x'' > 8/-16 = -1/2

d) x/ x-1 < 1

x ≠ 1