Question

The sum of a natural number and its square is 156. Find the number.

Answer 1

Let the required natural number be x.

According to the given condition, 

x + x² = 156 

⇒ x² + x – 156 = 0 

⇒ x² + 13x – 12x – 156 = 0 

⇒ x(x + 13) – 12(x + 13) = 0 

⇒ (x + 13)(x – 12) = 0 

⇒ x + 13 = 0 or x – 12 = 0 

⇒ x = –13 or x = 12 

∴ x = 12   ...(x cannot be negative)

Hence, the required natural number is 12.