Question

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

Answer 1

Let the two numbers be $x$ and $y$

$\Rightarrow x+y=1000$ ....(1)

$x^2-y^2=256000$

Using identity $x^2-y^2=(x+y)(x-y)$

$\Rightarrow (x+y)(x-y)=256000$.....(2)

$\Rightarrow x-y=256$ .....(3) [Substituting $x+y=1000$ ]

Adding (1) and (3) we get,

$2x=1256\Rightarrow x=628$

Substituting $x=628$ in (1)

$628+y=1000\Rightarrow y=372$

Therefore, the two numbers are 628 and 372.