What will be the Sum of the Number? If

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

  1. 30
  2. 36
  3. 33
  4. None of these
Nitin Baudh Learner Asked on 7th August 2015 in Maths.
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1 Answer(s)

Answer: (3) 33

Explanation:-
Let the three consecutive number X, X + 1, X + 2
According to the question,
X2 + (X + 1)2 + (X + 2)2 = 365
X2 + X2 + 1 + 2 X + X2 + 4 + 4 X = 365
3 X2 + 6 X + 5 = 365
3 X2 + 6 X + 5 – 365 = 0
3 X2 + 6 X – 360 = 0
3 (X2 + 2 X – 120) = 0
3 (X2 + 12 X – 10 X – 120) = 0
3 [X (X + 12) – 10 (X + 12)] = 0
3 (X – 10) (X + 12) = 0
Each factor are equal to zero.
Then, X – 10 = 0
X = 10
Then, Three numbers are X = 10, X + 1 = 10 + 1 = 11, X + 2 = 10 + 2 = 12
The sum of three consecutive numbers = 10 + 11 + 12 = 33.

Hence, the answer is (3) 33.

Anurag Mishra Professor Answered on 7th August 2015.
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