Find two consecutive numbers whose squares differ by 33

Two consecutive numbers whose squares differ by 33 are 16 and 17

Step-by-step explanation:

lets assume first number be x

since numbers are consecutive, so other number will be x + 1

From given information in question

(x + 1) ² - x² = 33

⇒ (x² + 1² + 2x) - x² = 33 [ since (a+b) ² = a² + b² + 2ab ]

⇒ x² + 1² + 2x - x² = 33

⇒ 2x + 1 = 33

⇒ 2x = 33 - 1

⇒ x = 32/2 = 16

so one number is x = 16 and other number is x + 1 = 16 + 1 = 17

lets recheck our solution

17² - 16² = 289 - 256 = 33, And since difference is 33, two required consecutive numbers are 16 and 17.