Question

Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.

Answer 1

Let the numbers be x-1, x, x+l . Then as per question, 

(x-1)² + (x) (x+l ) = 154 

⇒ x² -2x + 1+ x² +x =154 

⇒ 2 x² - x - 153 = 0 

⇒ 2 x² - 18x +17x - 153 = 0 

⇒ 2x (x-9) + 17 (x-9) = 0

⇒ (2x+17) (x-9) = 0 

⇒ As the number have to be natural number, x=9 

Hence, the numbers are 8,9 ,10 .