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Question
The difference between the squares of two consecutive numbers is 31. Find the numbers.
Solution
Let the numbers be x and x + 1 .
According to the question,
\[(x + 1 )^2 - x^2 = 31\]
\[\text{ or }x^2 + 2x + 1 - x^2 = 31\]
\[\text{ or }2x = 31 - 1\]
\[\text{ or }x = \frac{30}{2}\]
or x = 15
Thus, the numbers are 15 and 16 .
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