Question

Se x = 0,1212..., o valor numérico da expressão é:

a) 1/37

b) 21/37

c) 33/37

d) 43/37

e) 51/37

Answer 1

Resposta:

x=0,1212...   =12/99=4/33

(x+1/x-1)/(x²+1/x)  

(4/33+1/(4/33) -1)/[(4/33)²+1/(4/33)]  

=(4/33+33/4-1) /(16/1089 +33/4)

=(4*4/(4*33)+33*33/(4*33)-33*4/(33*4)) /(16/1089 +33/4)  

=[(16+1089-132)/132}/[ (64+35937)/4356]  

=(973/132)* (4356/36001)  

=4238388 / 4752132  

=4238388 / 4752132  

=128436 * 33/ (128436 * 37)  

=33/37

Letra C