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1/b = b/c = c/8 

Multiply all three sides by 8bc

8c = 8b² = bc²

Dividing 8c = 8b² through by 8 gives

c = b² 

Dividing 8c = bc² through by c gives

8 = bc

So we have the system of equations:

c = b² 
8 = bc

Substituting b² for c in 8=bc

8 = b(b²)

8 = b³

2 = b

Substituting in 

c = b² = 2² = 4

So,

b + c = 2 + 4 = 6   

So the correct choice is b + c = 6, choice B

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Check to see that

1/b = b/c = c/8

1/2 = 2/4 = 4/8

which is true. So it checks.   

Edwin