The difference 2 number is 3 and the difference between there square is 54 what are the numbers

Difference between the numbers = 3

Difference between their squares = 54

the numbers

Let the numbers be x and y. (x > y).

Difference between the numbers = 3

⟹ x - y = 3

⟹ x = 3 + y -- equation (1)

Also,

Difference between their squares = 54

⟹ x² - y² = 54

Substitute the value of x from equation (1).

⟹ (3 + y)² - y² = 54

(a + b)² = a² + b² + 2ab

⟹ 3² + y² - 2 * 3 * y - y² = 54

⟹ 9 - 6y = 54

⟹ 9 - 54 = 6y

⟹ 45/6 = y

⟹ 15/2 = y

Substitute the value of y in equation (1).

⟹ x = 3 + 15/2

⟹ x = (6 + 15)/2

⟹ x = 21/2

Therefore, the two required numbers are 15/2 & 21/2.

I hope it will help you.

Regards.