Question

The difference between two numbers is 14 and the difference between their squares is 448 then find the numbers

Answer 1

let the two numbers are; x and x-14.

the difference of their squares are:
$x ^{2} - (x - 14) ^{2} = 448 \\ x ^{2} - x ^{2} - 196 + 28x = 448 \\ 28x = 448 + 196 \\ 28x = 644 \\ so \: x = 23$


thus, the 1st number is "23" and another is x-14 = "9".