Question

the sum of two numbers is 1000 and the difference between their squares is 256000 find the numbers

Answer 1

Let the two numbers be x and 1000-x;
so x²-(1000-x)²=256000
x²-1000000+2000x-x²=256000
x=1256000/2000=628
Therefore the numbers are 628 and 372.

Answer 2

x+y=1000,
x²-y²=256000,
as in equation 1,
x=1000-y,
put in equation 2
(1000-y)² -y²=256000,
1000000+y²-2000y-y²=256000,
744000=2000y,
y=744000/2000
y=372,
hence x=1000-372,
x=628,
y=372