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If = 
, which of the following must be true?
A.I only
B.II only
C.I and II only
D.I and III only
E.I, II, and III
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答案：
C
Algebra Rati
Equation I is true:
given
take reciprocals
given
use last two equations
Equation II is true:
Equation I (shown true)
multiply both sides by x
divide both sides by b
Equation III is false, since otherwise it would follow that:
from above
divide both sides by a
use Equation III (assumed true)
multiply both sides by b
From this it follows that Equation III will hold only if 
, which can be false. For example, if x = a = c = 1 and y = b = d = 2 (a choice of values for which 
are true), then 
and Equation III 
is , which is false.
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