Question

Three consecutive integers are such that sum of the square of second and product of other two is 161. Find the three integers. 

Answer 1

Let the three consecutive no. be x, x + 1 and x + 2 

(x + 1)² + x (x +2) = 161 

⇒ x² + 2x + 1 + x² + 2x − 161 = 0

⇒ 2x² + 4x − 160 = 0

⇒ x² + 2x − 80 = 0

⇒ x² + 10x − 8x − 80 = 0

⇒ x (x + 10) − 8 (x + 10) = 0

⇒ (x + 10) (x − 8) = 0 

If x +10 = 0 

x = −10

It is not natural number

If x − 8 = 0 

x = 8

∴ Consecutive nos. are 8, 9 and 10.