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Q.

The product of two consecutive positive integers is 306. The integers are [[1]] and [[2]].

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answer is 17, 18.

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Detailed Solution

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The product of two consecutive positive integers is 306. The integers are 17 and 18.
Given that the product of two consecutive positive integers is 306.
Let’s assume that n and n+1 are the two consecutive positive integers.
According to the given condition,

⟹ n (n + 1) = 306

⟹ n^{2} + n = 306

⟹ n^{2} + n - 306 = 0

⟹ n^{2} + 18 n - 17 n - 306 = 0

⟹ n (n + 18) - 17 (n + 18) = 0

⟹ (n - 17) (n + 18) = 0

⟹ n - 17 = 0 or n + 18 = 0

∴ n = 17 or n = - 18

We will choose the value

n = 17

because the product is of two positive integers.
So,

⟹ n = 17

⟹ n + 1 = 17 + 1

∴

n = 18

Therefore, the integers are 17 and 18.

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