The difference between the squares of two consecutive numbers is 31. Find the numbers.
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 .
Concept: Equations Reducible to the Linear Form
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The difference between the squares of two consecutive numbers is 31. Find the numbers.
13