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How many orderer pairs of integers (x,y) satisfy the equation (x)/(12)=(12)/(y)

User Jvdbogae
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Final answer:

To determine the ordered pairs satisfying (x/12) = (12/y), we need to find the factor pairs of 144. There are 7 positive and 7 negative factor pairs of 144, plus the (12,-12) and its counterpart, totaling 15 pairs.

Step-by-step explanation:

To find how many ordered pairs of integers (x,y) satisfy the equation (x)/(12)=(12)/(y), we start by cross-multiplying. This gives us xy = 12· 12, which simplifies to xy = 144. Since 144 is a perfect square, we know that there are several pairs of factors (both positive and negative) that can be multiplied to get 144. These pairs are: (1,144), (2,72), (3,48), (4,36), (6,24), (8,18), (12,12), and their negative counterparts. Thus, we find that there are 7 positive factor pairs and 7 negative factor pairs, plus the origin pair (12,-12) and its counterpart (-12,12). This gives us a total of 15 pairs.

User Mirezus
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