Question

The sum of two numbers is 1000 and the difference between their squares is 256000.Find the number.

Answer 1

a+b=1000
a^2-b^2=256000

But (a+b)(a-b)=a^2-b^2
1000*(a-b)=256000
a-b=256000:1000
a-b=256 => a=256+b

256+b+b=1000
2b=1000-256
2b=744
b=744:2
b=372

a=372+256
a=628

Answer 2

let the numbers are x and y
x+y = 1000 ----------------------------(1)
x²-y² = 256000
(x+y)(x-y) = 256000
x-y = 256000/1000
x-y = 256  --------------------(2)
(1) + (2)
2x = 1256
x = 628
y = 1000-628
y = 372