# 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:

- 30
- 36
- 33
- None of these

**Answer: (3) 33**

**Explanation:-**

Let the three consecutive number X, X + 1, X + 2

According to the question,

X^{2} + (X + 1)^{2} + (X + 2)^{2} = 365

X^{2} + X^{2} + 1 + 2 X + X^{2} + 4 + 4 X = 365

3 X^{2} + 6 X + 5 = 365

3 X^{2} + 6 X + 5 – 365 = 0

3 X^{2} + 6 X – 360 = 0

3 (X^{2} + 2 X – 120) = 0

3 (X^{2} + 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.