Question

The sum of squares of two consecutive odd natural numbers is 394.
Find the numbers.
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Answer 1

Answer:

13 and 15

Step-by-step explanation:

Let the smaller number be n. The larger number will then be n + 2.

Since the sum of the squares of these two numbers is 394, we can write:

n^2 + (n + 2)^2 = 394

=> n^2 + n^2 + 4n + 4 - 394 = 0

=> 2n^2 + 4n -390 = 0

=> n^2 + 2n - 195 = 0

=> (n + 15)(n - 13) = 0

=> (n + 15) = 0, or (n - 13) = 0

=> n = -15 , or n = 13

Since n is a natural (non-negative) number only n = 13 is valid.

Therefore, the two numbers are 13 and 15