If the product of three consecutive positive integers is equal to their sum, then what would be the sum of their squares?

Correct option is B

Given:

• Product of three consecutive positive integers = their sum
• We are to find the sum of their squares

Concept Used:
Let the three consecutive integers be:
x – 1, x, x + 1

Solution:

• Product = (x – 1) × x × (x + 1)

• Sum = (x – 1) + x + (x + 1) = 3x

Product = x(x² – 1) = x³ – x
Given: x³ – x = 3x
=> x³ – 4x = 0
=> x(x² – 4) = 0
=> x = 0, x = 2, or x = –2

Only x = 2gives positive integers.

So the numbers are: 1, 2, 3

Their squares are:
1² = 1, 2² = 4, 3² = 9

Sum of squares = 1 + 4 + 9 = 14

Correct Option: (B) 14