The difference between two numbers is 14 and the difference between their squares is 448. Find the numbers.
Let the two numbers be x and y.
According to question -
x - y = 14.....(1)
x2 - y2 = 448.....(2)
From equation (1), we get -
x = y + 14.....(3)
Substitute the value of x in equation (2), we get -
(y + 14)2 - y2 = 448
⇒ 28y + 196 = 448
⇒ 28y = 252
∴ y = 9
Substitute the value of y in equation (3), we get -
x = 23
Thus, the numbers are 23 and 9.