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## The product of the least and greatest of three consecutive negative odd integers is 221. Find the three integers.

Question

The product of the least and greatest of three consecutive negative odd integers is 221. Find the three integers.

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Mathematics
1 month
2021-08-15T04:53:52+00:00
2021-08-15T04:53:52+00:00 1 Answers
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## Answers ( )

Answer:Step-by-step explanation:Square Root of 225 is 15 (with -15 also it would work but let’s stick to positive root)

Now, the 1st Odd Number is 15 -2 = 13 and the 3rd Odd Number is 15 + 2 = 17.

The required Numbers are 13 and 17.

This works for 3 consecutive Even Numbers also.

Why does it work?

Because, if we have 3 numbers to be a-2, a and a+2 (Doesn’t really matter if a is positive or negative)

(a-2)*(a+2) = a^2 – 4

So, you see adding 4 to the Product of the 1st Number and the 3rd Number (a^2 – 4 + 4 = a^2) gives you the square of the Middle Number, which is a^2!