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Question

The product of two consecutive positive integers is 306. We need to find the integers.

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Solution

Let two positive integers be n and (n+1)

n(n+1)=306

n2+n306=0
n2+18n17n306=0
n(n+18)17(n+18)=0
(n+18)(n17)=0
n+18=0 (OR) n17=0
If n+18=0n=18
Since, n is negative. So n=18 cannot be exist.

Now, lets take n17=0

n=17

n+1=18

Therefore, required positive integers are 17 and 18.

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