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