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Question : The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is:

Option 1: 30

Option 2: 33

Option 3: 36

Option 4: 45


Team Careers360 14th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

Correct Answer: 33


Solution : Let the consecutive numbers be (x – 1), x and (x + 1).
According to the question,
(x–1) 2 + x 2 + (x+1) 2 = 365
⇒ (x 2 – 2x + 1) + x 2 + (x 2 + 2x + 1) = 365
⇒ 3x 2 = 365 – 2
⇒ 3x 2 = 363
⇒ x 2 = 121
⇒ x = 11
So, the numbers are 10, 11 and 12.
The sum of the numbers = 10 + 11 + 12 = 33
Hence, the correct answer is 33.

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