Given:
Difference between the numbers = 3
Difference between their squares = 54
Find:
the numbers
Solution:
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.