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If = image.png, which of the following must be true?

image.png

    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

o and Proportion

Equation I is true:

 image.pnggiven

 image.pngtake reciprocals  

image.pnggiven

 image.pnguse last two equations 

Equation II is true:

image.pngEquation I (shown true)


image.pngmultiply both sides by x


image.pngdivide both sides by b


Equation III is false, since otherwise it would follow that:

image.png from above

image.png divide both sides by a

 image.pnguse Equation III (assumed true)  

image.pngmultiply both sides by b

From this it follows that Equation III will hold only if image.png , which can be false. For example, if x = a = c = 1 and y = b = d = 2 (a choice of values for which image.png are true), then  image.pngand Equation III image.pngis , which is false.

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