resolva as inequações produtos e quociente :
a ) ( -x+1 ) . ( 5x+2 ) ≥ 0
b) -x . ( 2x-1 ) . ( x - 3 ) < 0
c) (1-2x)*(3+4x)
------------------ ≥ 0
4-x
d) x
------- ≤ 1
x-1
(essas linhas *sinais de menos* sao o traço da divisao)
Soluções para a tarefa
Resposta:
a) (-x + 1 ) . (5x+ 2) ≥ 0
p=-x+1 ...raiz =1 ..a=-1<0
p++++++++++++++++(1)----------------------
q=5x+2 ..raiz x =-2/5 ..a=5>0
q------------------------(-2/5)+++++++++++++++++
Estudo de sinais:
p++++++++++++++++(1)----------------------
q------------(-2/5)+++++++++++++++++
p*q---------(-2/5)++++(1)----------------------
-2/5 ≤ x ≤ 1
-------------------------------------------------------------
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 .....x≠4
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 ....x≠1
p=x-1 ..raiz x=1 a=1>0
p-------------------(1)+++++++++++++
x < 1