(GERATRIZ DE UMA DÍZIMA PERIÓDICA) Se x = 0,1212..., o valor numérico da expressão: (imagem)
é:
a) 1/37
b) 21/37
c) 33/37
d) 43/37
e) 51/37
é:
a) 1/37
b) 21/37
c) 33/37
d) 43/37
e) 51/37
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Verified answer
A=0,1212...100a=12,12,12...
100a-a=12,12,12... -0,1212....
99a=12
a=12/99=4/33
(x+1/x-1)/(x²+1/x)
[(x²+1-x)/x] /[(x³+1)/x]
(x²-x+1)/(x³+1)
***(x+1)³=x³+3x²+3x+1
***(x+1)³=x³+3x(x+1)+1
***(x+1)³-3x(x+1)=x³+1
***(x+1)[(x+1)²-3x]=x³+1
***(x+1)[x²+1-x]=x³+1
(x²-x+1)/(x+1)[x²+1-x]
=1/(x+1)
fazendo x= 4/33
=1/(4/33+1)=33/37
Letra C