Question

Resolva as inequações.Ajudaaaaa....​

Answer 1

Resposta:

45)

a) x²-2x-3 ≥0

a=1 > 0 , concavidade para cima +++++++++(x')-------------(x'')++++++++++

x'=[2+√(4+12)]/2=(2+4)/2=3

x''=[2-√(4+12)]/2=(2-4)/2=-1

++++++++++++(-1)----------------------(3)++++++++++++++++

-1 ≥  x  ≥ 3   é a resposta

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b) (x²-1)*(x+6)>0

p=x²-1 ==>a=1>0, concavidade p/cima +++++++++(x')-------------(x'')++++++++++

x²-1=0 ==>x=±1

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

q=(x+6) ==>raiz=-6 ..a=1>0 é crescente --------------------(x)++++++++++

q-----------------------(-6)++++++++++++++++++++++++++++

Estudo de sinais:

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

q---------(-6)++++++++++++++++++++++++++++++++++

p*q-----(-6)++++(-1)-------------(1)+++++++++++++++++++

(-6,-1) U (1,+∞ )  é a resposta

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c) (-x²+2)/(2x-6) ≤0             ...2x-6≠0  ==>x≠3

p=-x²+2 ==>a=-2<0 , concavidade p/baixo ------------(x')+++++(x'')---------

-x²+2=0 ==>x'=±√2

p---------------------(-√2)+++++++++++++++(√2)------------------------------

q=2x-6 ==>a=2>0 , crescente ----------------(x)+++++++++++++

2x-6=0 ==>raiz=3

q--------------------------(3)++++++++++++++++++++++++++

Estudo de Sinais:

p-----------(-√2)++++(√2)------------------------------

q------------------------------------------(3)+++++++++++

p/q+++++(-√2)-------(√2)++++++(3)------------------

-√2 ≤ x < √2   U  x> 3   é a resposta