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 y respectively
x+y=1000
x=1000-y

x^2-y^2=256000

(1000-y)^2-y^2=256000

1000000-2000y+y^2-y^2=256000

-2000y=256000-1000000

-2000y=-744000

2000y=744000

y=744000/2000

y=372

x=1000-372

x=628

Therefore, the two numbers are 628 and 372 respectively

Answer 2

x+y=1000
x2-y2=256000
but x2-y2=(x+y)(x-y)
256000=1000(x-y)
x-y=256
x=256+y
now x+y=1000
256+y+y=1000
2y=1000-256=744
y=372
x+y=1000
x=1000-372
x=628