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
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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