17.the difference between the squares of two consecutive numbers is 31. find the numbers.

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.